Problem is, finish9's kids want to shoot sports, so you can't use slow shutter speeds. What's worse, they're talking about indoor sports. And even though they're indoor, they'll still need something on the order of 100 mm for most shots (35mm film equivalent focal length).
No substitute for big aperture and sensitive (high ISO) sensor, unfortunately. Even image stabilization and a tripod will be of marginal use. The only other thing that could help, as another poster has said, is a good flash, at least for subjects closer than about 40 feet.
Any way you cut it, it sounds like $$$ to me.
I know......But another poster on here asked a question and i was answering that.