Gakuen Babysitters
Love So Life (Is Romance, but it feels like things mostly revolve around the kids from what I remember)
already know those, if you have something that's action lmk!! it doesn't need to have babies, like orv for example
Mr villains day off
Kono oto tomare
Mercenary enrollment
Probably the more mainstream ones will give you that, like Fairy Tail, Bleach, Hunter x Hunter, ect. I haven't really read any of those personally, and am only going off of the animes, so I am not sure. But you could try Noblesse. That one I have read and can recommend.
recs for mc's that care about their companions, im looking for any genre except romance, where the plot revolves around familial bonds without them actually being family