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.
Mairimashita! Iruma-kun
Youkai Gakkou No Sensei Hajimemashita!
Sakamoto Days
Chronicles Of The Martial God
There was a Hero
I'm a Martial Art Villainess but I'm the Strongest!
Tondemo Skill de Isekai Hourou Meshi
Not as much but these two may be worth it...
Mr. Devourer Please Act like a Final Boss
Sword Sheath's Child
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