One of the games I like to do with competitive or upper level rec kids is the handstand circle. Half the gymnasts stand in a smallish circle, with the other half of the gymnasts in a larger circle, paired with a gymnast in the inner circle. The gymnasts in the inner circle kick up to handstand, and the gymnasts in the outer circle can help their partner balance by holding their legs. When you call "switch" the gymnasts in the outer circle rotate in one direction, to help the next inner circle gymnast holding handstand. This way, their handstands get stronger, and they learn to balance on their own, although they can still get some help.
However, if the outer gymnast tries to "switch" too quickly, they will likely push their partner over. I usually make some penalty for gymnasts who fall, like holding a push-up shape, but this would depend on the group of kids.
At the end, of course, you switch the inner and outer circle so everyone holds handstand.