My nephew will be 10 this month. He was given a Mossberg 20ga two years ago. He's shot it and handled it well for the most part but it isn't the easiest for him to carry or handle in the stand.
This year I went deer hunting for the first time and went with him. I took my 300blk pistol. He liked it a lot. I know it isn't traditional and many don't even know you can use them but I think it would be perfect for a kid. My 15 year old daughter also liked the idea better than her 20ga.
Walking the fields and woods with an AR pistol slung across my chest was pretty nice.
I plan to build another 300blk pistol this year.
I would politely disagree on recommending a handgun. A handgun is much more difficult to shoot accuratley than a rifle. There is also a much higher possibility of having the muzzle pointed at something it shouldn't be pointed at.