You've received a lot of good advice here. As others have said, don't rule out the 20 gauge before determining if you can reduce the recoil. You don't need magnum loads. You may find that a better recoil pad will help. Ask a competent gunsmith what else you can do to mitigate the recoil.
As far as the .410 goes, I plan on trying to get a gobbler with the pipsqueak shotgun, but I've been hunting turkeys for over 40 years and some people caution even me against it. I agree with others that the .410 can do the job, but I wouldn't put it into the hands of a first-time hunter.
Your goal should not be to get your son a gobbler. Your goal is to give him the best turkey hunting experience you can. You want to give him the experience of calling a gobbler in close, of learning from watching the gobbler, of bonding with him in the hunting experience, and of bonding him to the idea of hunting. Anything else -- including killing the gobbler -- is gravy.
A .410 will require precise shot placement. That's language we usually use for rifles, but shooting at a called-in gobbler is more like rifle shooting than shotgun shooting. You must hit the head with enough pellets having enough penetration to kill the big bird.
A crossbow can do the job with a body shot out to 40 yards or more in the hands of a competent shooter. In the hands of a 9 year old, that range is reduced simply because of the shooter's lack of experience under live target conditions and his lack of experience in shooting at varying shooting positions and angles. I'd figure the range for a crossbow on a live target in the hands of a 9 year old is 20 yards -- about the same as with a .410 in the same hands.
I think the 20-gauge is still your first option. You have plenty of time to figure out how to mitigate recoil, and what load to use. Examine the stats on energy with various size pellets at various ranges, and don't try to stretch the range on a live gobbler.
Also, build up to the 20-gauge. Start with a .22. Transition to a .410. Then have him shoot something like a .223 or a .243 rifle. Help him to understand the principles of recoil -- it's more than the opposite reaction to a bullet or load coming out of the barrel, but start there. When you move on to the 20 gauge, wrap yourself around himi at the bench so that your larger body and stronger arms and hands can control more of the recoil so his little body doesn't have to. Take him shooting at least once a week, twice if possible, and he'll be ready when the time comes.
The point to teach him is that recoil is nothing to be afraid of, that all of us have a limit to the recoil we can take. Make sure he's wearing ear protection even when shooting a .22 rimfire.
Don't give up yet on the 20 gauge. With almost 2 months to go I think the boy can be ready to shoot that, and to shoot it well.
Steve.
