Stopford succeeded his father as 2nd Earl of Courtown in 1770. He had served as a member of Parliament for Taghmon from 1761-1768, and was Treasurer of the Household and Lord of the Bedchamber to the Prince of Wales. On 7 June 1796, he was created Baron Saltersford, of Saltersford, Chestershire. He married Mary Powys of Suffolk [d. 1810] in 1762. Among their four sons was James George, who would become the 3rd Earl of Courtown.