Rick,
Why don't you ask the kid what he likes? And offer a little guidance along the way. I gave my nephew a swede in 6.5 when he was about that age. His father cut the stock down for him. A 30/30 or .32 special is a good choice. A Savage 99 in .243, .250 or .300 is good.
If the kid likes a bolt gun, a short rifle in .243 or .257 Roberts can be a good choice.
When we were that age we all had rolling blocks in .43 Spanish! easy to carry, anyway.
What the kid might enjoy more is if you went along. You could cook and keep camp, or kind of amble through the woods and move the deer around for him.
jn