Graham Coghill coached 34 seasons at St. Peter Chanel High School in Bedford, Ohio. While at Chanel his program won five state team titles and had seven runner-up finishes. Under his leadership, coaching staff and wrestlers qualified for the state tournament 157 times and 117 were state place-winners. A wrestling room was built by the "Chanel Wrestling Family" of wrestlers, parents, family and friends and dedicated to Graham. St. Peter Chanel was later closed and demolished.

Graham is one of only three coaches to have a state champion in all three divisions.

He was also involved in youth wrestling since 1971, helping run the Longwood YMCA and Firebird Youth wrestling programs.

After Chanel closed, Graham coached Nordonia High School in Macedonia, Ohio for three years. Since 2020 he has helped coach the wrestling program at Walsh Jesuit School.