Carmody was born on August 24, 1933, in Shreveport, Louisiana.[2] In high school, he received three letters in football and baseball from Holy Cross High School in New Orleans, Louisiana, from 1948 to 1952.[2] He attended college at Copiah-Lincoln Junior College from 1952 to 1954 and Tulane University from 1954 to 1955.[2] While at Tulane, Carmody was a two-year football letterman who played in the first night game at Tulane Stadium in 1954.
Carmody was hired to replace Bobby Collins as the Golden Eagles head football coach in 1982 after Collins took the head coaching position at SMU.[5] Under Carmody's tutelage, the Golden Eagles compiled a record of 37–29 with no bowl appearances.[6]
During Carmody's tenure, the Golden Eagles defeated Alabama, 38–29, in Tuscaloosa in 1982, snapping the Crimson Tide's 56-game home winning streak at Bryant–Denny Stadium.[7][8] It was the first time since 1962 that Alabama had lost there, and 1982 proved to be the final season of coach Bear Bryant's career.[9] Carmody recruited a Kiln, Mississippi, high school quarterback named Brett Favre to Southern Miss in 1987.[10]
In 1984, Southern Miss, already under NCAA sanctions for prior infractions, admitted to improper recruiting practices pertaining to freshman linebacker Don Palmer.[11] As part of the fallout, Carmody's salary was frozen. Palmer alleged he was given clothing, basketball game tickets, cash, and transportation to the campus by an USM assistant coach.[11]
Later coaching career
After leaving Southern Miss, Carmody returned to Mississippi State to serve as defensive coordinator under head coach Rockey Felker, a position he held during the 1989 and 1990 seasons.[2] Under his watch, the Bulldogs defense improved from 89th nationally before he arrived to 15th.[2] He then returned to Ole Miss to serve as associate head coach and defensive line coach under head coaches Billy Brewer and Joe Lee Dunn, where the Rebels defenses ranked #6 nationally in 1992, #1 nationally in 1993 and #17 nationally in 1994.[2] New head coach Tommy Tuberville did not retain Carmody on his staff in 1995.