Try a rabbit stopper, may cost a little bit in the replacement co2 bulbs but will provide hours of fun and a snitch of the price of a pcp.
Light, no recoil so your young un wont loose interest from not being accurate and most of all it will hold its value to sell on. You can then move up to a springer, when he has the muscles , or make the investment to a pcp.
A rat-catcher with a stock may be an alternative, or if your wanting to spend some money and can find one, something from the brocock range.
As 8shot says a meteor is a good starting springer, but my young un struggled for a t