He coached at Rhode Island State College (now the University of Rhode Island) from 1920 to 1948 and taught a style of basketball using a fast-breaking offense and a full-court defense. In his 28 years at Rhode Island, Keaney never had a losing season. In 1939, Keaney's Rams became the first college team to average more than 50 points per game, and in 1943 the team had an average of more than two points per minute (80.7 points per game), which led to the Rams being dubbed "The Firehouse Gang." During his tenure the Rhode Island team was invited to the National Invitation Tournament (NIT) four times. Keaney's career record was 401-124 (.764).
In 1946 the Boston Celtics hired Keaney to be their first head coach. Keaney's doctor, however, refused to let him take the job. He remained as Rhode Island State/URI's athletic director until 1959. The school color, "Keaney Blue," was his creation.
URI named the Frank W. Keaney Gymnasium-Armory in his honor in 1953. Keaney was inducted into the Naismith Memorial Basketball Hall of Fame in 1960. He is also a member of the Helms Basketball Hall of Fame, the New England Basketball Hall of Fame, the State of Rhode Island's Heritage Hall of Fame, the Providence Gridiron Club's Hall of Fame, the Bates College Scholar-Athlete Society and the University of Rhode Island Athletics Hall of Fame.