Most river and ocean stones are not nice and round, but there really are a few round ones on every cobble beach and riverbank. If you have kids or know some kids, they would probably love to help you treasure hunt for nice rocks.
The black beach rocks along the ocean near my house are nicely rounded but they are chock-full of holes because they are all lava rocks. I could fill the holes with something like acrylic molding paste (a.k.a. modeling paste) and then paint them, but I instead purchased a bag of smooth, white limestone river/ocean rocks from Indonesia. You may be able to purchase nice river rocks from somewhere that sells landscaping materials.
Also, there are paintable wood, plaster, and unglazed ceramic eggs and balls available in craft stores that could work with stone painting techniques.