Cooper was the son of Marks and Etta Temerson Cooper. He graduated Phillips High School and then attended Harvard University and Harvard Law School. From 1937 to 1940 Cooper clerked for Supreme Court Justice Hugo Black before returning to Alabama to practice law.
During World War II Cooper enlisted in the U.S. Navy. After the war he continued to practice as a partner in Cooper, Mitch & Crawford, focusing on labor relations. He was active in the CIO's "Operation Dixie" organizing drive, and represented the United Steel Workers of America in several actions. He won a landmark case for Black railroad workers in 1951.
In 1963 Cooper was asked to facilitate the transfer of donated funds to bail out young people arrested during the Children's Crusade, forestalling further public demonstrations. Most of the funds were recovered when the criminal cases were dismissed. Later that year Cooper was one of 244 attorneys who worked with President John Kennedy to establish the Lawyers' Committee for Civil Rights under Law.
- Erdreich, Ellen Cooper (March 14, 2017) "The legacy of my father, Jerome 'Buddy' Cooper." The Birmingham News
- Smith, Jay (August 1, 2017) "Bull Connor, Martin Luther King Jr. and the Labor Movement AFL-CIO Blog - accessed November 25, 2019