I recommenda .410 shotgun at his age. Remington made a youth pump that was recently discontinued butis still available new. It still might be toolong for a 7 year old and a little pricey, but a single shot with a youth stockshould definitely be a gun that he can learn tohold and shoot.
.410'sare agreat way to teach a youthhow to hunt and shoot because the pattern of a 3 inch.410 shellis easier to shoot game withthan a .22 LR, since perfect accuracy isn't required with it's more open pattern. Also 3 inch .410 shellsloaded with#6 shot are veryeffective. If3 inchersare too powerful for him to shoot, then hecan always hunt withthe 2.5 inchshotshells until he's ready for the longer ones.
Installing a red dot on a.410 for him would be very cool, especially for shots at moving game. The single shot gunsare inexpensive enough that a red dotcan beadded and it will still be affordable!