Cunningham attended Holy Cross College and Catholic University of America, graduating with a bachelor of arts in 1931. He went to medical school at the universities of Munich, Heidelberg and Frieburg in Germany and was certified in clinical pathology and pathological anatomy at the Boston University School of Medicine in Boston, Massachusetts in 1941.
He opened a private practice, Cunningham Scott and Bishop, in Birmingham in 1942. It was the first laboratory accredited by the College of American Pathologists, which he helped to establish, and survives as Cunningham Pathologists.
Cunningham was a member of the Mountain Brook Club and St Paul's Cathedral. He has served as president of the Alabama Chapter of the American Cancer Society. He was inducted into the Alabama Healthcare Hall of Fame in 2006. He is buried at Elmwood Cemetery.
- "Joseph Anthony Cunningham" obituary (June 5, 2009) The Birmingham News
- Joseph A. Cunningham, M.D. at the Alabama Healthcare Hall of Fame