"Covenant children" are the children of believers — treated by Scripture as heirs of the covenant promises and members of the covenant household. The Abrahamic covenant explicitly included "thee, and thy seed after thee in their generations" (Genesis 17:7); the sign of circumcision was applied to infant sons. Peter on Pentecost: "For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call" (Acts 2:39). Paul addresses children directly within his epistles to the churches (Ephesians 6:1; Colossians 3:20) — treating them as part of the gathered congregation, not outside it. Reformed paedobaptists ground infant baptism on this covenant-children theology.
(Composite.) The children of believers, treated as heirs of the covenant's promises and members of its household.
Reformed and many other traditions emphasize covenant children: the children of believers are not strangers to be evangelized but covenant members to be discipled into mature faith.
Differences exist among traditions about the proper sign for them (paedobaptism vs. credobaptism), but the underlying conviction — that children of believers are claimed by the covenant — is broadly shared in Scripture.
Genesis 17:7 — "And I will establish my covenant between me and thee and thy seed after thee in their generations for an everlasting covenant."
Acts 2:39 — "For the promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call."
Deuteronomy 6:6 — "And these words, which I command thee this day, shall be in thine heart: and thou shalt teach them diligently unto thy children."
Ephesians 6:4 — "And, ye fathers, provoke not your children to wrath: but bring them up in the nurture and admonition of the Lord."
Modern Christianity often imports market-style evangelism for its own children; Scripture treats them as covenant heirs to be raised in the faith.
The Christian household's task with its children is principally discipleship, not evangelism. Acts 2:39 says the promise is unto you, and to your children. The covenant claim runs through the family.
This does not absolve the children of personal faith — each must, in time, embrace the covenant for himself. But the household's default posture is to assume the covenant's reach over its children and to disciple them accordingly.
Hebrew banim (sons) and zera (seed) cover the Old Testament terminology.
Hebrew zera — seed, offspring; the covenant's generational reach.
Greek tekna — children; in Acts 2:39 of the covenant's extension.
"The promise is unto you, and to your children."
"The household's default with its children is discipleship, not evangelism."
"The covenant runs through the family; the family runs through the covenant."