Greaney was a three-year starter on the Holy Cross men's basketball team, serving as co-captain during his senior year in 1981-1982. He helped lead the team to an overall record of 72-43 (.626) over the course of his career, with the Crusaders advancing to the NCAA Tournament once and the National Invitation Tournament twice. During his senior year, Greaney led the team in scoring with an average of 14.4 points per game, and was named first team All-ECAC. He finished his career with 1,150 points, including a high of 28 against Boston College during his senior year, and ranked as Holy Cross' 18th all-time leading scorer. upon graduation Between his junior and senior seasons, Greaney was a member of the NIT All-Star team which toured Columbia and the Dominican Republic. He also received the Richard J. Maloney Award from the Varsity Club in 1982, as the basketball team's MVP.