Admittedly, I didn't read every post to see if anyone else said this. The 'low recoil' rifle has so many factors. It still drives me insane that manufacturers release rifles in 243, 7mm-08, etc and they do so.in these pencil barrel, plastic stock 5.5-6.5 lb variety with 20-22" barrels. These are almost exactly what isn't best for the smallest of shooters. I fell for it once and bought a 243 youth model, and it was one of the snappiest recoiling rifles I ever had. Don't do it!
Knowing that it won't likely be the youngster actually carrying the rifle afield, take the opposite approach. Look for heavier and/or install a muzzlebrake. You can always get an inexpensive stock that is completely adjustable (stocks At-one or similar) to perfectly fit their small stature, and then put the factory stock back on when they grow up (which will happen fast). Or, it you are totally committed to buying a lightweight rifle in a mild cartridge, take the butt plate off of it and fill it full of BBs ($12 at tractor supply) and put the butt plate back on. This will add 2-4 lbs to the rifle which will make a huge difference in a 243 or 7mm-08, or.308. If you reload, the world is your playground for reduced loads. If not, Hornday reduced recoil line of ammo is awesome for small youth. Please don't make the mistake of putting a youngster or first time shooter behind a lightweight rifle under the pretense that it is 'just a little 243', as physics dictate the outcomes more than marketing hype.