You would need gearing that will allow the pull force to be manageable by the power of the chosen motor, and some lever to release the pull. Hundreds of ways to do it, you have to think according to the parts you can gather.
A "L" shape hook at the end of a string being wound on the motor shaft can do the pull and hit a ramp at the end of the pull changing its angle to allow slipping the pulled part out of the "L"
And dozens of other ways.... if the release has to be automatic.
Now that sounds like a good physics problem. Small tires would have little thrust, and too big would have little velocity. Selecting the right tire size would be key. Hmm, off to the drawing board.
The smallest motor can do this if it spins up a flywheel which supplies the impulse of energy to throw the ball. Do the math on paper first. You need the weight and you need to calc. the required "muzzle velocity."