Copley was the son of Copley Amory [1841-1879], and the nephew of Edward Linzee Amory [1844-1960]. The younger Copley was the great-great grandson of the artist, John Singleton Copley. He and his wife, Mary Forbes Russell Amory [1870-1961], had five children: Copley Jr., Henry Russell, Katharine Amory Smith, Walter, and Elizabeth Cole Amory.
Linzee, John William. The Linzee Family of Great Britain and the United States of America. 2 vols. Boston, 1917: 2:796.