It is important to notice that there is not a single verse anywhere in the Bible that tells us to exclude children from the covenant. What we see through the biblical writings is that Children are always included with the parents in the covenant. And this inclusion is important to God. He said at the beginning of the history of the covenant with Abraham, " And I will establish my covenant between you and me and your offspring after you throughout their generations for an everlasting covenant, to be God to you and to your offspring after you" (Gen. 17:7). So here we have an everlasting covenant that includes children. He inspired the apostle, on the very day that the covenant became new, to proclaim as gospel, "the promise is unto you, and to your children... even as many as the Lord our God shall call" (Acts 2:39). Rebuking His unfaithful wife, Judah, in Ezekiel 16:20-21, God states, like as a Husband and Father, “ And you took your sons and your daughters, whom you had borne to me, and these you sacrificed to them to be devoured. Were your whorings so small a matter that you slaughtered my children and delivered them up as an offering by fire to them?” In Malachi 2:15, God condemns the divorcing that was prevalent in Judah because divorce jeopardizes the "godly offspring." (And still today the unchangeable God hates divorce in the covenant community because it is destructive of the children who, as covenant children, are His children.)
The importance of our children's inclusion in the covenant is displayed all throughout the gospels. Jesus welcomed the children to himself, which is welcoming children into his covenant. Luke 18:15–16, Now they were bringing even infants to him that he might touch them. And when the disciples saw it, they rebuked them. But Jesus called them to him, saying, “Let the children come to me, and do not hinder them, for to such belongs the kingdom of God.” The word used for ‘children’ is paidion which is used exclusively to describe very young or infant children. When Jesus says “let young children come to me, and do not hinder them, for to such belongs the kingdom of God” this is clearly covenantal language - as no one comes to God except through covenant. Jesus’ inclusion of children into the people of God is prolific in the gospels. There is no example where Jesus tells parents to consider their children unsaved until they can repent and believe. There is no spirit in the text of keeping children from participating in the worship of God with the people of God. Does God receive praise from the lips of unbelievers? No. yet he does receive praise from the lips of infant children. Matthew 21:15-16, 15 But when the chief priests and the scribes saw the wonderful things that he did, and the children crying out in the temple, “[Hosanna] to the Son of David!” they were indignant, 16 and they said to him, “Do you hear what these are saying?” And Jesus said to them, “[Yes]; have you never read, “ ‘Out of the mouth of infants and nursing babies you have prepared praise’?” Is there ever a suggestion in the gospels or anywhere in the NT that we should keep our children from addressing God as Father? Father being a covenantal privilege. In Mark 10:16 after calling the children to himself took the children in his arms, placed his hands on them and blessed them. This is what Jesus does to those who are his own, should we really think that those children were not part of the covenant because they were not old enough to make a personal choice? Mark 9:36 continues this theme when Jesus “… took a little child (infant) whom he placed among them. Taking the child in his arms, he said to them, “Whoever welcomes one of these little children in my name welcomes me, and whoever welcomes me does not welcome me but the one who sent me.” Into what is Jesus telling us to welcome this child?
Paul writes in Ephesians 6:1–4, Children, obey your parents in the Lord, for this is right. “Honor your father and mother” (this is the first commandment with a promise), “that it may go well with you and that you may live long in the land.” Fathers, do not provoke your children to anger but bring them up in the discipline and instruction of the Lord. The Law was given to and was for the covenant people of God. The fifth commandment is given to children (covenant members). Paul affirms this commandment for children, thus affirming the children’s inclusion into the covenant. He then builds on this covenantal inclusion of children when he writes to fathers saying, “…bring them up in the discipline and instruction of the Lord.” He does not say bring them to the discipline and instruction of the Lord, but to bring them up in this covenantal reality.
Along these same lines we see in Titus the qualification for elders which include having believing children Titus 1:6, if anyone is above reproach, the husband of one wife, and his children are believers and not open to the charge of debauchery or insubordination. If we view our kids as unbelievers until they reach the age of accountability, then it would follow that fathers of young children cannot be pastors or elders. However, if we believe that children are included in the covenant, they are objectively Christian because they are in the covenant.
As faithful Christian parents, we should take great comfort from Acts 2:39: “the promise is for you and for your children,” and rest in the reality that God’s promises are multi-generational. Paul’s assurance that children even of just one believing parent are “holy” (1 Cor. 7:14) ought to reinforce our confidence in God’s inclusion of children in the covenant. Acts 16:31 should also bring us great rest and comfort as parents when Paul says, “Believe in the Lord Jesus, and you will be saved, you and your household.”