Kids can handle a lot more than you give them credit for. When i was 9 i got my first .22 rifle. I shot it a good bit, but we didn't live in an area where we could shoot much. I didn't shoot for around 2 years after that. When i was barely 13 i started really getting into guns. I was a skinny 120 pound 5' 2" kid. My first new gun that i shot was a 1911, i was nervous, but i did it, and after the first shot i really begun to enjoy it. After that i shot a .357 mag. I shot one with a long barrel and to my dismay it had almost no kick. After that i got real confident i shot an ar15, an ak47, and a .308, I was expecting the .308 to have a lot more kick. When i went shooting the next week i decided to shoot the Win. 94 in 30-30 and i thought it had a good amount of kick, but nothing i couldn't handle, nor was it painful. Then i shot my first 12 gauge shotgun, i thought it had quite a kick, but it didn't hurt but i felt like i could handle the more powerful loads, so i tried them, and they had a good kick, but i could handle and enjoy shooting it. Then i wanted to shoot a .44 mag, I felt like i could conquer the world so i decided to shoot it with the magnums not the specials to start, It had a kick, it hurt a little bit to shoot, but the feeling of "being a badass" outweighed the kick, so i decided to shoot it with one hand... Even if i was 3 inches and 25 lbs smaller i feel like i could of handled most of what i shot.
All of this is to show that a kid can handle a hell of a lot more than a .22 or other small calibers. I would say how about a sks, or if you really love him a sig 556 in 7.62x39 or a rock river lar47. or heck even an ak, but for a younger person the primary concern shouldn't be recoil, it should be weight. Also for a good lightweight ak a cz vz68 sporter. 7.62x39 Is a good caliber for him (in my opinion) because it doesn't kick hard, it is designed for the ranges you are hunting deer in, and it's cheap to shoot.