Tell you what. After watching countless dad/son/daughter combos at the range the past few years, I've come to the conclusion that bolt actions get boring...really quick.
Instead, have a look at the Henry lever action. It comes in youth sizes and let me tell you...this thing is a LOT of fun. Light, quick shooting carbine and the racking makes it interesting.
New (kid) shooters really shouldn't start out with a semiauto IMO due to safety reasons, and that's where the Henry shines. It has to be racked every shot, and Dad can be sure the gun stays pointed downrange with each controlled shot.
I've since put a small red dot on mine and it really ups the fun factor. Keep both eyes open, line up the dot on the target and watch that can dance.
My first 'gun' was a Red Ryder bb gun. It was a hoot, and at 40 years old I decided to re-visit my childhood favorite.
On a side note I bought a regular Plinkster in 2007 and couldn't get that thing to feed at all, even with the extra magazines I bought. Let's just say that WalMart firearm return policy is...lacking.