Most AR are .223 of 5.56, but they also make them in other calibers. All you need to do is switch uppers. Your right about most ranges, but there are some ranges that allow .223.
I really think the best option is a regular 10/22 (around $230) and a few cans of Tactical Krylon (yes they make it) it a few camo colors for your kid to customize it. I also like the Ruger Target Tactical (around $400). It is a 10/22 target rifle in a black Hogue stock, target trigger and a bipod. You still have to buy optics for the Target Tactical, but optics for a .22 can be inexpensive. I'm going to buy .22 drop in for my AR and a Target Tactical when I sell a couple Busses (anyone interested in a NMSFNO, OJ Game Warden, bone handled Cultie, Hortonized Muskrat, or NMFBM

).
[youtube]DZuQv52BrSU[/youtube]