Joseph Saville Cony (1834 – 10 February 1867) was an officer in the United States Navy who served during the American Civil War. The Fletcher-class destroyer USS Cony (DD-508) was named in his honor.
Cony was born in 1834 in Eastport, Maine. He was appointed acting ensign 3 November 1862. He commanded several successful small-boat expeditions along the Carolina coast while serving on the USS Western World and as executive officer on the USS Shokokon. Promoted to acting master 7 September 1863, Cony was honorably discharged 7 November 1865, and was lost at sea off Cape Hatteras on 10 February 1867, when his merchant command City of Bath burned and sank.