I shot my first deer when I was about his age with my dad's 308. I would say as long as he can line up and see out of the scope he should be able to shoot whatever you see.

If you are gonna add ont to the safe I would go 7/08 with 120gr bullets over the .243 very little recoil difference in the two and alot more bang for your buck in my opinion, but the .243 is a great round as well. Kacee likes em both. She started with .243 at 7.

My son started with a 30-30 when he was 8. I bought manages recoil but found that he didn't need them. My dad started me off with a 30.06 :

My first deer hunt was with a .270 at age 10. I got scoped right in the center of my forehead and it took several years to get over that mental block of shooting a bigger rifle.

Letting an 8 year old shoot a .270 is the worst thing you can possibly do to to have a chance of dampering his enthusiasm for hunting. Let him shoot a gun he is COMFORTABLE shooting without being scared, nervous, or recoil-shy. My suggestion would be a .223, but apparently there are a lot of guys on here who think letting a 8 year old shoot a .270 is good idea when in actuality there is ZERO advantage to doing so.

My son will be upgrading this year he has a single shot .243 that you could probably have . If you are interested let me know and I will talk to him. Through the years I have taught my boys to get goods use out of your possessions and then pass them down for others to get use out of . He has dropped pigs with this gun , no issues with them running off, the gun I getting to short for him now so I think we are going to move him up to a 30.06.