The Ruger American rimfire can be had with the youth stock, and it comes with an insert that makes it more like a full size rifle, and they use 10/22 magazines. I've had two and they were both awesome, I gave one to my niece when she turned 8 to celebrate her getting to come hunting with us for the first time. She shot it great then, and it fits her great now as a tall for her age 14 year old. For reference, she shoots a standard size Savage 11 in 260rem now that she draws her own tags.
When her younger brother hit the same age, I got him a 10/22 takedown (I stumbled into the takedown for a great price, I was after a regular 10/22). I gave him one 1-shot magazine, and a couple 10s, so he could learn with the single until he was ready for more. The 10/22s are just so light and easy to handle and have an almost unlimited aftermarket, its tough to beat them for kid use.
The Tactical Solutions Owyhee is such an awesome little 22, its on the expensive side but a special rifle. Its essentially a bolt action 10/22 Takedown. Its so small and light it really feels like a toy. I also really like the Tikka T1x, its a shame that its a little big for small kids, and there aren't many small stock options.