Cooper was the son of Kenny and Stella (Raines) Cooper of Harman, Randolph County, West Virginia. His family was among the first settlers of Randolph and Pendleton counties, and these roots in the Appalachian mountains had an impact upon his music.
While in high school, Cooper was a member of the Leary Family Singers. In 1939 he married Wilma Lee Leary. They became Wilma Lee and Stoney Cooper, one of the biggest country music acts of the 1940s through the 1960s. They had one daughter, Carol Lee Cooper.
In 1947, they were cast members of WWVA Jamboree in Wheeling, West Virginia until 1957. Their band was called The Clinch Mountain Clan. In 1948, Cooper signed a recording contract with Columbia with the help of Fred Rose that lasted to 1955. In 1954, Cooper joined the Grand Ole Opry.
In 1973, Stoney's health began to fail; he suffered a series of heart attacks and spent long periods in the hospital. Finally, he suffered a heart attack on 4 February 1977, from which he died in the intensive care unit of a Nashville hospital on 22 March 1977.