Free: Contests & Raffles.
You can't go wrong with a 243 (unless elk is one of the primary species on the menu). If you think you need more horsepower, jump up to the 308. Or as Bob33 posted, the 30-06 will work good with the special light recoil loads. Only problem I see with that is a 30-06 could very well be too long and/or too heavy for a 9 year old.
http://www.remington.com/product-families/ammunition/centerfire-families/managed-recoil.aspxThis will make a 30-06 recoil about like a 243. When he grows up, no need for a new gun.
m77 youth .260rem