Cunniff's extensive experience with USA Hockey includes serving as associate coach during the 1994 Winter Olympic Games in Lillehammer, Norway, assistant coach for the 1998 U.S. Olympic Men's Ice Hockey Team in Nagano, Japan, and assistant coach for the 2002 U.S. Olympic Men's Hockey Team in Salt Lake City, Utah. Cunniff was named assistant coach for the United States team that captured the championship in the 1996 World Cup of Hockey. He was an assistant coach for four U.S. National Teams (1982, 1991, 1992 and 1993) at the International Ice Hockey Federation (IIHF) Men's World Championships, and was an assistant on two U.S. National Junior Teams (1992 and 1993) at the IIHF World Junior Championships. In addition, Cunniff was an assistant coach for Team USA in the 1981 Canada Cup tournament.