It would be my contention that the primary ground for infant baptism is drawn from the nature of the covenant of grace which includes the children of believing parents. So the Westminster Larger Catechism states:

Q. 166. Unto whom is baptism to be administered? A. Baptism is not to be administered to any that are out of the visible church, and so strangers from the covenant of promise, till they profess their faith in Christ, and obedience to him,^[1] but infants descending from parents, either both, or but one of them, professing faith in Christ, and obedience to him, are in that respect within the covenant, and to be baptized.^[2] 

However, since Baptists insist that Christians who baptize their infants are adding to and even defying the biblical command to baptize, I believe that, in addition to defending the inclusion of infants with believing parents in the covenant of grace, we should meet them on their own ground and show them that, in fact, it does not and cannot support their contention. 

1) It is true that there is no command in the Bible to baptize the infants of believers particularly. Nor is there a command in the Bible to not baptize these infants. So a prohibition must be inferred as it is nowhere stated in scripture that infants of believers may not be baptized.

2) However, the Baptist replies that scripture requires faith and repentance before baptism may be administered and therefore it obviously excludes infants.^[3] In effect, what the Bible commands speaks sufficiently. Yet there is actually no passage in scripture that says that we may only baptize those who confess their faith. It still must be inferred from the command to baptize that infants must be excluded by the nature and content of that command. 

3) Indeed what scripture requires is that new converts be baptized but that does not address the question as to what is to be done with their children. The Baptist again infers that the children of converts are covered under the original command (which in effect is a ban on baptism for some or a generalized restriction) but that is gratuitous.^[4] To approach baptism in this way would be to exclude everyone but those who originally heard the gospel.^[5]  

4) Furthermore, we must see that the command to baptize is both general and particular. In cases particular, that is where the command is given to some, whether en masse or individually, it comes in the context of the preaching to those who are estranged from God. But in the case of the apostles, who were commanded to baptize, the requirement comes more generally. Thus in Matthew 28:19 we read that Jesus said that his church ought to baptize the nations.^[6] Here is, prima facie, an inclusive command to incorporate groups of people into the church, rather than just individuals. Thus more than those who believed could be included in the command to baptize even though when the command was published it was presented in a way to focus on those who had yet to believe on Christ. That is to say it was necessary for the command to be published in this way for, as both Baptists and Presbyterians agree, no one should be baptized who is not in some way under or in the covenant of grace. They divide only as to whether the application of baptism also extends to those who belong by way of covenant household. If the original hearers had not or would not believe, then baptism for their infants would be a moot point. 

5) This is also demonstrated by the example of the apostles or in their application of the more general command to baptize. In the books of Acts, as well as Corinthians, we see that groups or, in these cases, households, were inducted into the fellowship of the church through baptism (see Acts 16:15,33 & 1 Corinthians 1:16).^[7]  

6) That a command for believers or those who are repentant to be baptized  cannot exclude children of believers is seen by way of comparison to other biblical commands that would seem to exclude children:

No one in his right mind will deny that infants ought to be fed. We read in Isaiah 1:19, “If ye be willing and obedient ye will eat the good of the land.” And in 2 Thessalonians 3:10, we read that Paul commanded “that if any would not work, neither should he eat.” Infants cannot be willing and obedient; infants cannot will to work; therefore infants have no right to eat. Willingness, obedience and work do not apply to infants; therefore infants are not to eat. Ridiculous, you say; and so it is. But this is the logical outcome of the argument we are examining.^[8]

In short, the Baptist misapplies the command to be baptized by making it narrower than it was meant to apply. Though it is true that some of the particular demands connected to baptism cannot be applied to or fulfilled by infants,^[9] this does not mean that the general command to baptize cannot be applicable to infants and fulfilled by the requirements of God’s word that parents do for their children what they cannot do for themselves.^[10]

7) Let us note the use of the passive voice in the command to those who would be recipients of baptism: “be baptized.” Note the contrast to the active voice of the command to partake of the Lord’s Supper: “take, eat.” The passive voice implies a reception of the sacrament without active resistance (consistent with infants and young children) in addition to receiving it in a manner that is a consistent with its nature (submitting to the ordinance of the Lord in repentance, or not actively and purposely resisting the meaning of such: Luke 3:3 & 7).^[11] The active voice of the Lord’s Supper, in addition to requiring a physical act which infants cannot do (take and eat)^[12] and (by its active nature) cannot be done for them or on their behalf, as it requires them to do something which they are not aware of (examine themselves). This is different from a sovereign action of God where He saves the child by His spirit because it is merely receptive whereas the former is reflexive and thus requires participation.

8) Additionally, there are other commands that scripture holds out to us as applicable to the children of believing parents in a way that supports their inclusion in Christian baptism. For example, “Children, obey your parents in the Lord” (Ephesians 6:1). Here the apostle Paul applies the fifth commandment in the context of Christian homes which assumes a relationship “in the Lord.” The relationship exists because all that a Christian has and does is under the lordship of Christ. As such, the command to baptize must include their children since it is done in the Son’s name who claims them as his own with their parents (Matthew 28:19 cf. Matthew 19:13-14).

9) If Jesus commanded that the children be allowed to come to him and not be turned away from his blessing (Matthew 19:13-14) then they should also receive the sign of His blessing (see Acts 2:38ff.). Undoubtedly the former is greater than the latter since the sign merely typifies the reality so how can they be forbidden from partaking of the sign when the reality is promised to them too?

10) If Jesus said that the reception and example of infants and children was like unto the kingdom of God (Matthew 18:2-6 & 19:14) then they should also receive the sign of the kingdom (see Matthew 28:18-19), that is we argue from the greater to the lesser.

11) But, some may ask, why is there no a clear command that encompasses children of believers? Why did God not simply say: baptize infants? One may ask that question of the paedobaptist but he should not feel he is required to answer it in order to prove his position anymore than the Baptist must tell us why God has not made it explicitly clear (by way of prohibition) that infants must not be baptized. Indeed, why does God do anything that He does? It must be left to the secret counsel of God as it is His wisdom to conceal a matter (Proverbs 25:2 cf. Romans 11:33). But what the question we must answer is as follows: is the matter sufficiently clear as to establish a doctrine or practice based on multiple scriptures, either by inference or explicit teaching?^[13] To me it is abundantly clear that God has not forbidden infants of believers to be baptized and that the command to baptize, as scripture requires, can be fulfilled by them in accordance with their covenant membership.^[14]

1. Acts 8:36-37, Acts 2:38.
2. Genesis 17:7&9 compared with Galatians 3:9,14 & Colossians 2:11-12 and with Acts 2:38-39 and with Romans 4:11-12. 1 Corinthians 7:14, Matthew 28:19, Luke 18:15-16 & Romans 11:16. Westminster Confession of Faith. Glasgow, Free Presbyterian Publications, 1997, page 256.
3. If covenant children can be influenced by or acted upon by the Holy Spirit, then it is not impossible for them to be saved (however much that may be invisible to the eye of the believer). See Psalms 22:9-10, Psalms 71:6, Jeremiah 1:5 & Luke 1:41. Furthermore, the scripture is abundantly clear that the old covenant sign of salvation was applied to children who had no knowledge of their sins, let alone salvation in Christ by faith: Deuteronomy 30:6, Romans 4:11 & Colossians 2:11-12.
4. “[Scripture] never once mentions the administration of baptism to adults who were born of Christian parents.”  Bavinck, Herman. Reformed Dogmatics, Volume 4. Grand Rapids: Baker Academic, 2008, page 526. It is especially gratuitous because a positive command does not, by its nature, exclude, even if it is impossible for those who hear it to obey it. Consider that though the law was weak through the flesh (Romans 8:3) but that does not mean that the law does not have to be kept (Romans 3:19-20). In this case, the law is kept on our behalf by another and therefore the command is not negated but upheld.
5. We might also add that such a requirement excludes servants of the household as well (unless they personally repented) but they were baptized on the basis of a believing (covenantal) representative (see Acts 16:33-34 cf. Genesis 17:10-14).
6. cf. Isaiah 52:15 “So shall he sprinkle many nations; the kings shall shut their mouths at him: for [that] which had not been told them shall they see; and [that] which they had not heard shall they consider” (emphasis mine).
7. Note too how this principle follows in light of Jesus’ example to minister to households: Luke 8:40; 9:10; 10:5; 18:15-17; 19:10
8. Swan, Thomas. Water Baptism: What Saith The Scriptures? Middle to Me. Andrew R. Middleton. Web PDF, page 5. August 26, 2017. www.goo.gl/R6zzZU
9. Or at least as far as we know (see footnote 3).
10. Such as prayer, Bible reading, leading them to Jesus and other such requirements for which covenant parents are responsible (see 2 Timothy 3:14-16).
11. In this way it parallels the dual administration  of circumcision which was applied to the infant and the non-resisting adult. It may be presumed that if the adult or older child resisted circumcision they would be cut off from the people of Israel (see Genesis 17:14).
12. Whereas they can, passively, receive baptism.
13. By way of comparison, the doctrine of the Trinity is found in the pages of scripture though it is not explained with that name and in one text in particular.
14. In addition to what we have considered above, consider the following scriptures that speak to the inclusion of infants with believing parents in the covenant of grace: Genesis 17:7, Deuteronomy 30:6, Psalms 103:17 & 128:3, Isaiah 54:13, Jeremiah 32:38-40, Malachi 2:15 & 1 Corinthians 7:14.