Born to Philip and Julia Cohen, Cooney changed his last name before entering professional baseball. He played in a single major-league game in 1905 as a third baseman for the New York Highlanders and thereupon became the first Jewish member of the New York Yankees’ franchise. He went hitless in three at-bats. While playing second base for the Omaha Rourkes on July 7, 1917, he turned the first unassisted triple play in Western League history.
Cooney played minor-league ball for 17 seasons before retiring in 1920.