John Henry Greene, born in Cleveland, Ohio, and Irene Cecelia Fallon, born in Pennsylvania, were a young couple who married in Cleveland. Their fathers, Daniel John Greene and Patrick John Fallon, were born in Cleveland, and Philadelphia, Pennsylvania, respectively. A popular local Cleveland legend tells that Danny J. Greene was the son of Irish Catholic immigrants, but his parents were native-born in the United States. His ancestors on both sides were ethnic Irish.