My advice is to steer clear of any high velocity spring/piston airguns, especially the inexpensive ones.
First, these are going to be difficult for kids to cock. Second, they are going to be quite difficult to shoot well. The thumb/hand through the stock grips make it even more difficult, for one tends to grip the rifle harder, which is contrary to the technique needed for spring airguns. Third, unlike the higher end rifles, these are not going to be as easily rebuilt, tuned, nor last a few lifetimes.
ETA: For one of the best easy to shoot and cock spring airgun for the kids would be the Weihrauch HW 30, but these are .177 and good for critters up to starlings. The next step up in power, which would be fairly easy to shoot well would be the HW 50. The Wehrauch HW 50 can be had in .177 or .22.
The other way you could go would be to get something like a Benjamin Maximus or Benjamin Discovery with hand pump. These PCP air rifle will cost a bit more but you do get several shots before having to pump the rifle up. They will also be quite easy to shoot well.