He toured England in 1966 with the West Indian team but did not play Test cricket. A right-arm fast bowler, Cohen made his first-class debut for Jamaica in 1963-1964. In that season and the next two he played 15 matches and took 27 wickets.
He played club cricket in England in 1965, taking 33 wickets at an average of 13.84 for Smethwick in the Birmingham and District League, and 17 wickets at 18.64 for Warwickshire Second XI. He was not in the original selected team to tour England in 1966, but when Lester King had to withdraw, Cohen was selected to replace him.
He was the youngest player in the team The established pace trio of Wes Hall, Charlie Griffith and Gary Sobers played all five Tests, and Cohen played in 18 of the 22 other first-class matches, taking 40 wickets at 24.22, with his career-best innings figures of 6 for 71 against Sussex.
King returned to the team when the West Indians toured India in 1966-1967. Cohen led the Jamaican bowling in the Shell Shield later that season, with 15 wickets at 31.86, but played no further first-class cricket thereafter.