I don't think that in your backyard or garage you're going to be able to make a biodegradable adhesive that has the strength to stay attached to a car. Even more, you're not going to be pressing and firmly adhering the ball to the surface, but hoping that you can throw with enough accuracy and strength to cause it to stick. Also, spheres have very little surface area to attach something to, unless they flatten out.
Cool idea, but I don't think there's much feasibility in it.