My wife used to do that.

Then when we had a newborn/infant, they would lay on my belly and fall asleep to the rhythm of my breathing.

Then when the kid was a bit older, but still little enough that I could hold them and rock them, I would sing some songs while artificially deepening my voice and rocking them. They fell asleep so fast almost every time. Their favorite / the most effective were
Little Bird Little Bird
and especially
Love Street

Unfortunately, neither of those really work anymore - still, listening to them again to make sure I was remembering the right ones put a memory lump in my throat. Especially because both wife and daughter just left for a weekend beach trip.

Maybe this wouldn’t be a good time to put on Futurama …