Savage makes some youth rifles with scope packages. I'd check them out. Single shots like others said would be a good idea cause they are typically inexpensive and you could cut the stock.
I was in Sports world the other day and I picked up a HOWA off of the demo rack and it had a really short length of Pull, and it was only like $369. I had picked it up because I had been reading about accurate factory rifles and their name kept coming up. So I am guessing it was a youth model of some sort. I think it might have even had a scope, but I picked up several so it might not have either.