As a college player for the Boston College Eagles, Cunniff averaged 2 points per game. The left-winger then embarked on a long career playing in the minor leagues, never making it to the NHL. Cunniff then turned to coaching. He briefly led the Hartford Whalers in the 1982/1983 season, and went on to become assistant coach with the Boston Bruins. He then joined the New Jersey Devils franchise, first as a head coach (1989-1991), later also in various other functions. In addition, Cunniff served on the coaching staff of three U.S. Olympic teams (1994, 1998 and 2002). He died of throat cancer.