Well, Claire in Claymore has to take care of a boy.
Just kidding, I know you’ve watch it already.
How about
The Baby and I? (edit: it seems that this series is also known as
Aka-chan to Boku,
Baby and Me, or
Me and My Brother. It's called Baby and I in my country). It’s about a single father and his eldest son who have to take care of the baby youngest son. Problems ensues and they have to struggle to make it. There’s no mother though (which is the point of this series). It’s melancholic and funny too. It’s a 90s slice-of-life anime.
There is also
UFO Baby which is like a more funny and hilarious version of The Baby and I. It deals with a boy and a girl who have to take care of an extra-terrestrial baby ^_^.
Hmm....I didn't see
Beelzebub in your anime list. That fighting-action shonen is quite popular already.
Also, to some extent, there is
Konjiki no Gashbell. The child-babysitting in this series is not that dominant, though.
The last time I post in your thread was just several days ago and here I met another.
You do like to marathon anime don’t you?