I got my daughter a Remington R-25 when she was 9, in 7mm-.08. I removed the stock and put a AR-15 adjustable stock on it, so it would fit her. That year, I used reduced recoil rounds and she was fine with it. Because it is semi auto, it dosen't kick like a bolt rifle, but it wouldn't eject the reduced recoil rounds.
When she turned 10, she started using regular/normal loads, and they eject fine.
She is a small kid, now 12 and weights less than 75lbs and has had no trouble with that gun. She has killed everything she has shot with it.
If you wanted a bigger caliber for a kid, I would highly suggest something on a AR-10 type platform that's semi automatic. Just put a nice recoil pad on the stock and he will be fine. If he complains, tell him there is a small girl in NC that's been dropping deer like a bad habbit since she was 9, with no complaints. Lol