Is there a single basketball game, ever, that would use trackball? Your probably going to have to find some other item that happens to be 3" round (or whatever your trackball size is) and try to make it work.
Perhaps you can find an actual mini-basket ball that size and fill it with something heaver than air...

(really stretching there).
If you were a good painter, you may be able to paint a white/clear one? Or if they have an orange one, you could just paint the black "basketball stripes"? ... although finding a paint that won't rub off will be tough ...