Conroy followed in the footsteps of his father and two uncles in playing hockey at Clarkson University for the Golden Knights. He enrolled at Clarkson in 1990 and played four seasons for the school. During his junior season of 1992–93, Conroy scored two goals in a 5–3 victory over Rensselaer Polytechnic Institute in the Eastern College Athletic Conference (ECAC) semi-final to help lead his team to the conference championship game. Conroy reached 100 career points with the goals, joining his father Mike as the only such pair in Clarkson's history to reach that milestone. Conroy and the Golden Knights then won the ECAC title with a 3–1 victory over Brown University.