I have several .243's (Browning BLR, H&R Heavy Barrel, Remington 700 BDL, Weatherby Vanguard)...I think a 243 loaded with 100g Partitions is damnear impossible to beat for a deer gun...my 8 year old daughter hunts with the Weatherby and my Niece also hunts with a Weatherby Vanguard in 243 as well. Great caliber, low recoil, accurate....
I will add like someone else that a 7mm-08 is also a great low recoil, accurate, youth option and my daughter shoots my Savage 11 in 7/08 without trouble as well except the stock it too long for her to hunt with it.
Be sure to find a rifle in a youth stock...when my brother and I bought the Weatherby Vanguards in 243 they offered a package with both youth and adult stocks...haven't seen them since but was a deal too good to pass up.