After an amateur career that saw him win international tournaments in England, Wales and Scotland as well as a New York Golden Gloves title and have a record of 55 wins and 3 losses, Cooney decided to turn professional, being signed by promoter Don King.
Cooney's first paid fight came on February 15 of 1977, beating Billy Jackson by a knockout in one round in New York. Nine more wins followed and Cooney started gaining fame as a future contender. Then he stepped up in class and fought future world Cruiserweight champion ST Gordon in Las Vegas, winning by a fourth round disqualification. Cooney's star kept on rising with 11 more wins in a row, spanning 1978 and 1979. Among the people he beat were former George Foreman victim Charlie Polite, The former United States Heavyweight champion Eddie Lopez (The Animal), and Tom Prater.
When 1980 came, Cooney was already being featured on national television and rising some national attention. He beat title challengers Jimmy Young and Ron Lyle, both by knockout. By this time, he was ranked number 1 in the WBC and challenging Larry Holmes into a fight.
Then 1982 came and Cooney's life changed. Holmes agreed to fight him, with a purse of one million dollars for the challenger. Cooney, who was attempting to become the first white World Heavyweight champion in 23 years, was, perhaps unwillingly, involved in the middle of a promotion that took racial overtunes, as Don King nicknamed him The Great White Hope. The fight then took a circus atmosphere, and many boxing fans worldwide became interested. In what would be one of the biggest HBO Boxing productions in history, the fight was broadcast to over 150 countries around the world.
Cooney lost his bid to become World Heavyweight champion by a knockout in 13 rounds, and took off one year. Finally, when he was set to come back in late 1983, he got cut during sparring and had to lay off for another year.
In September of 1984 he finally stepped into the ring again, beating Phillip Brown by a knockout in 4 rounds in New Orleans. He fought one more time and won, but personal problems took him away from the ring again.
In 1987, he made a one fight comeback to meet former World Heavyweight champion Michael Spinks, losing by a knockout in five rounds, and in 1990, in Cooney's last fight, he lost in two rounds to former world champion Foreman.
In what could be considered an ironic twist, Cooney began an organization which has helped boxers get jobs after they retired. This could be called ironic, because among the boxers Cooney's organization has helped, many of them are, black. Cooney has always tried to distance himself from the racial overtones the promotion towards his fight with Holmes had, and he and Holmes have become very good friends over the years.
Cooney and Alex Ramos, a Puerto Rican who won the United States Middleweight title in the 1980s, are the leaders of the organization, named FIST. Cooney also enjoys signing autographs for the people who remember him.
Cooney compiled a professional record of 28 wins and 3 losses, with 25 knockouts.