The Copley baronetcy of Sprotbrough in Yorkshire was created, for the second time, on 27 August 1778, for Joseph Copley né Moyle, grandson of Sir Godfrey Copley, 2nd Baronet of the first creation. He was the son of Catherine Copley, daughter of the 2nd Baronet, and her spouse Joseph Moyle the elder; a Clerk of the Signet, he was heir in 1766 to the Sprotbrough estate, and at this point changed his surname to Copley.
The 2nd Baronet was Member of Parliament for Tregony from 1796 to 1802. The title became extinct on the death in 1883 of the 4th Baronet.