Shotguns were mentioned in Percy Jackson and the Olympians. However, both the make and model of these guns are unknown.
When Percy Jackson fights Ares on the beach in San Francisco, the police arrive and tell them to drop their guns. Percy comes to the conclusion that the Mist made the police see his and Ares' swords as shotguns.
During the Battle of Manhattan, Percy's mother wakes up and takes a shotgun from a police car and blasts a giant, who flies twenty feet backward into Nico di Angelo's sword. When Percy demands to know when she had learned to fire a shotgun, she responds saying, "About two seconds ago."
A Mossberg 500 is kept in the shed at the back of Athena's cabin. It was offered by Annabeth Chase to Piper McLean as her weapon, but she turned it down because it didn't fit her. Annabeth agreed, reasoning it would probably be too flashy. Piper notes that Annabeth checked the pump, "like it was no big deal." This suggests that celestial bronze shells exist seeing as how a standard shotgun shell would most likely have not have the ability to kill a monster.