28 gauge is the superior low-recoil option, especially if you get a gun properly scaled for it (and not just 28ga barrels on a 20ga frame). Lighter than 20ga and will pattern far better than .410.
Stay away from Stoeger coach guns. Too much kick in 20ga to be very fun for a young kid, and made like shit. Mine disassembled itself the first time I shot it, and I sold it after I fixed the abysmal machining mistakes that caused the problem. Look at the Mossberg O/U for budget, or the Cabela's exclusive Rizzini if you don't mind spending more. Both are available in 28ga, as well as .410 and 20ga if you prefer the inferior options.