Dropping Fossils can be found in Dark Fossil Rocks in basically any dig site. They are almost worthless in the beginning of the game, selling at 1G, but if you go visit the Hare Club at Cranial City on Cranial Isle and talk to the man on the right, he will introduce himself as John Guano (HA-HA) and will have a proposition for you. Every time you bring him a certain amount of Dropping Fossils to him, he will give you a prize. Once you are supposed to bring him 20, he will give you a Miraculous Fossil Rock.