Word for parent of a single child?
Perhaps the closest is uniparous:
- (of certain animals) producing a single offspring at each birth
- (of a woman) having borne only one child
- botany (of a cyme) giving rise to only one branch from each flowering stem
From Parity (biology) also primipara:
a woman who has borne but one child or who is parturient for the first time.
I offer one-time:
He’s a one-time father.
The verbs “to be a mother” and “to be a father” mean to deliver a child as a parent. Even if a person is already a parent, they can still “be a parent” again:
I’m going to be a father for the second time.
Oddly, some people seem to use this to refer to labour, not count of children:
She’s a one-time mother of beautiful twin girls.
It also generalises well (and is way more commonly heard) with higher numbers:
Mary was a three-time mother, one-time grandmother, and all-around excellent woman.