Umm well... remembering my childhood... a lot of shows that I watched weren't that kid like
I mean there was always action and fights... like Spiderman, X-men... So it is a bit hard for me to say what would suit for your child...
Though when I was completly a kid, I was obessed with Tom & Jerry 0_0
However, don't know any animes like that...
I think
Sonic X would do quiet well.
Obviouse names would be Pokemon and Digimon which probably almost everyone were watching as kids...
K-on maybe? Pretty innocent series in my opinion... well we do have characters in swimsuits several times but nothing major...
Sadly can't come up with anything else...
How old is your child exactly?