You'll have to hunt a bit to find one, and they may not be quite right for a really little fellow, but when I was a kid I wanted one of these so bad I could taste it. I stared at the picture in the Sears-Roebuck "wish book" for hours. Why if I'd had one of these, there wouldn't have been a rustler dare show his face, in Hanover County, Virginia in the mid 60's (1960's that is).
Ithaca M-49 Single Shot. The magazine tube you see there is fake. It's a falling block single shot that is more fun than you can shake a stick at. And a good shooter too.
When I was a kid, my mother was afraid of rifles. She just knew if you shot one into the ground at your feet, you'd kill someone in China. Shotguns were Ok, but no rifles.
So I didn't get one until I saw this one last year. It's quickly becoming my favorite 22 rifle, even if the sights are kinda blurry these days.
They show up on Gunbroker regularly. I believe they did make a "youth" model of the same gun.