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Ira Berlin says that about one third of the enslaved population lived in two-parent families. (I was not able to find figures specifically concerning children.)
While family separation was a pervasive aspect of slavery, it would be a mistake to assume that all families were destroyed. There are many instances of enslaved spouses and children living together on the same plantation, sometimes even in the same cabin. Some slaveholders encouraged such arrangements, believing that a stable family life would make their slaves more contented and productive. The pattern of slaveholding in the Chesapeake in the early years of the nineteenth century probably reflected the general situation throughout the slaveholding South. In this region, approximately one-third of the enslaved population lived in two-parent families.
(Ira Berlin, Many Thousands Gone: The First Two Centuries of Slavery in North America)
This roughly corresponds to the way another researcher describes the life of adult women:
Most slave women lived in nuclear or extended families on the same plantation, and if their families were disrupted, they worked hard to establish new ones. In the late eighteenth century, only about 20 percent of all African American women lived in nuclear families with a husband and children. About 50 percent lived in extended families or had close ties with siblings and other kin. The remaining 30 percent lived alone, most often as a result of death or forced migration. But even those women who did not live in nuclear families forged important and lasting bonds with kin and other slaves, forming a network of people who provided emotional and social support.
(Deborah Gray White, Ar'n't I a Woman?: Female Slaves in the Plantation South.)