Cuneo began his first grade career for North Sydney in 1957. In 1961, Cuneo was selected to represent NSW City against NSW Country. Cuneo spent a total of 6 seasons at Norths before switching to Newtown in 1963. Cuneo played his one and only finals game for Newtown in 1966 against Manly which ended in a 10-9 loss. Cuneo retired at the end of 1969 after 119 first grade games. He then went on to coach the Newtown reserve gradeside in the following years. He died on 7 January 2014.