I don't know what guns you have access to but here is what I've done with my 63 pound 10 year old:
1) When he was 7 or 8 I introduced him to the .22. No recoil & cheap. Started with a scoped 10/22, but then had him shoot another .22 with peep sights and even a scoped .22 pistol. It didn't take long before he was shooting these well. Nothing serious here, just controlled playing with an underlying theme: practice.
2) This fall I set up my Scoped Knight Wolverine for him. It is .54 cal and his first shot was 40 grains of 777 with a roundball. I kept that first powder charge low so his first impression would be "I can handle this". Next 2 or 3 shots were 45 grains of 777 and by the end of that day he was shooting 50 grains of 777 with no comments about any increased recoil. I took him out one more time for practice with this load. From a rest, I really felt a 50 yard shot would be no problem - he was shooting it quite well. Also, I shot the gun a few times with 60 grains of 777 & saw no change in the point of impact (you know where that is going, right).
It took us about 3 hunts during youth season to kind of figure out what the deer were doing. So on the 4th hunt we were about to set up in a field and noticed deer already there and coming slowly towards us. I had a simple folding chair for him to rest the gun on. A doe was almost in range when 4 more came out between us and the doe. I told him to aim for the spine of the closest (90 yards) and shoot as soon as it cleared the others. He did & the doe dropped at the shot. I expected that old round ball to drop some at that distance but it didn't seem to, so it was a spine shot. 60 grains of 777 & the roundball did fine - pass thru. I figured the load had similar ballistics to a .44 magnum. He shot another doe with this load a month & a half later.
I'll probably have him shoot 250 grain XTPs next year and as much powder as I can sneak in there without him complaining.
