Plenty of options out there. I've had mine as young as 8 with a .50 cal MZ. Just dialed the powder way back.
Teaches the kids to make an ethical shot, as they only get one chance at it.
The only thing I remind my kids, is that time in youth season is limited. I split my time between hunting with both kids, and my wife, plus wanting to hunt myself. They also choose to play soccer or run CC during the fall which impacts time in the field as well.