Apparently I’m not up to speed on the latest kiddie shows but LazyTown seems to have a strong following. They’ve just released a free game called Airship Challenge that has very cartoony graphics and it’s super light on violence. The description is merely “Fly the Sportacus Airship and navigate your way through the clouds over LazyTown collecting SportsCandy to earn points. Avoid the cannon balls or you’ll lose power!” So it’s as simple as tilting the phone to navigate and trying to pick up fruit while avoiding cannon balls.
It’s free and should be a hit with kids. You can check it out here.