Born in Orange, New Jersey, into a baseball family, Feeney was the grandson of Charles Stoneham, principal owner of the New York Giants from until his death in 1936, and the nephew of Horace Stoneham, who owned the team from 1936 through 1976 and transferred it to San Francisco in 1958. Feeney began his association with the Giants as a batboy, and after his graduation from Dartmouth College and military service during World War II he joined the team's front office at the age of 24 as vice president in 1946. Although he never held the official title of general manager, Feeney would function as head of the Giants' baseball operations department for almost 24 years.