You would think a kid would bounce all over the place but if you make the expectations clear and just start with short sessions I think you could make it work....there is another thing you could try too...it is flat on the bottom and spherical on the top like a ball cut about a third of the way down....it is filled with gel and not air so it is squishy and not bouncy but it gives sensory feedback.
Search for OT supply sites and you will see all sorts of seating discs and such...the nice thing about a disc is you can use it all over the place a ball would be hard to transport to the library and cafeteria, etc.
