I would not hesitate using the .44 mag out of a rifle. It is very effective for deer at close range even out of a pistol, so I don't see what the problem would be using it in a rifle. As you said, just limit the shots to 50 - 60 yards and use a .44 mag load that is tailored for deer hunting.

I understand about not wanting to make him recoil-shy by giving him too much gun at a young age. The .44 mag in a rifle with a nice recoil pad should be no problem to handle. Another option if it is possible for you would be a muzzleloader using a reduced powder charge and a lighter bullet - like a .40 cal 200 grain XTP with 60-70 grains of powder - very light recoil and very effective on deer at closer ranges (I've shot this bullet quite a bit).

I would not use the .410 for deer. My hunting buddy had his daughter use a .410 when she was younger and I saw firsthand the lack of effectiveness. She did take a couple deer with it, but it always involved some tracking as it did not kill deer quickly. After a couple years he switched her over to a muzzleloader with a reduced powder charge, and this worked much better.