He used the Chakra a lot and also his bow. I can't think of an occasion when he used his mace either as himself or an avatar.
Yes, Lord Vishnu used his Kaumodaki mace to kill a demon name Andhaka. The story is mentioned in Devi Bhagavata, Book 5, Chapter 6.
Wanting to kill Andhaka, Janârdana became infuriated, and, drawing his bow made of horn, call S'ârnga, shot at him arrows after arrows. The Dânava cut off all those arrows to pieces with his own mass of arrows. Then, becoming very angry, he shot fifty sharp arrows at Hari. Vâsudeva quickly made all those arrows useless and hurled Sudars'ana Chakra with thousand spokes on the Dânava with great violence. Andhaka thwarted this with his own discus and shouted aloud with such a great force that all the Devas became confused and confounded. Visnu's Chakra being baffled, the Devas became distressed with grief and the Dânavas got elated. Seeing the Devas thus grieved, Visnu held aloft his Kaumodakî Gadâ (club) and came hurriedly before the Dânava. Hari struck then with his Gadâ on the Dânava's head whereon he fell senseless on the ground.
The battle between Hirnayaksha and Varaha at the sea floor was fought with maces. I presume Varaha used His mace Kaumodaki. There is no mention of Varaha using the Sudarshana Chakra to kill Hiranyaksha in Srimad Bhagavad Mahapurana and the description iss of Him armed with the conch, discus and mace.