Rob, your message did make it into my T-Net Private Messages mailbox. Please pardon the delay in replying. I've had some health issues, and insomnia. Stone cannonballs do exist, but they are VERY difficult to authenticate with certainty. There's just too many round or round-ish stone "imposters" that were not manufactured to be an artillery projectile. Native American "game balls," and ancient and more-modern stone ornamentaion balls are examples of the imposters.
Stone was the first material used as a cannonball. But perfectly-round stone balls require a great deal of labor and time to manufacture. So, by the late 1500s, cast-iron had entirely replaced stone cannonballs. (However, Colonial-era naval ordnance records indicate there were still a few stone leftovers in the very early 1600s.)
A clue for correct ID... the type of stone is important. Due to the limitations of early-Colonial metal tools, it was extremely difficult to create a true sphere out of very hard stones like quartz or granite. Therefore, softer stone, such as limestone, was the preferred choice for cannonballs.
I should also mention... many round/roundish stones found on Colonial-era shipwrecks are simply ballast-balls... not cannonballs.
I used the term "perfectly-round" above, for an important reason in cannonball authentification. To roll down the bore of a cannonbarrel, and be fired out of it with explosive blast, a ball absolutely MUST be a perfect sphere (also called a "True Sphere"). Although a slight casting-mold seam is acceptable, any lumpiness or out-of-roundness can cause the ball to jam in the barrel during loading or firing, which is very bad news for the cannon's crew. Historically, part of an army or navy Artillery Ordnance Inspector's job was to make certain EVERY cannonball suplied to the gun crews is perfectly-round. Regardless of whether it's a metal or stone ball, if a ball isn't perfectly-round, it is not a cannonball. You can check for deviation from true sphericality with a good-quality Caliper.
Another clue in cannonball authentification is, the ball's diameter. To be a cannonball, it must precisely fit one of the known diameters of historical cannons. If there's no matchup size-wise, it's not a cannonball.
Another clue: If a ball is a cannonball, there should have been at least one cannon of the correct size in the area where the ball was excavated. (Unless the location was an "ammo dump" ordnance supply location.) For example, on Ebay, sellers advertize "cannonballs" allegedly found at the Gettysburg battlefield which are too large (or too small) to correctly fit into any cannon that was present at Gettysburg in 1863.