Do you have 200 dwellers in your vault? That's the current maximum.
I have this same issue.
Using my tablet: Started the game off with 1 male / 3 female in the living space. All three female become pregnant. Always have over 10 space available. Happiness is over 85% always. No kids for hours.
Played this game for maybe 30 minutes on my phone and had a kid.
Reboot my device. Built another living quarters. Within minutes had 2 kids.