Conroy began his career with Home Farm, where he won four Irish youth caps. He played for the Home Farm under-13s at the age of ten, at a time when Home Farm were considered the best youth team in the country. The club held the registration of much of the country's top young players, and future Ireland international Billy Newman played in the same age group as Conroy, though Conroy was determined to go beyond playing in the League of Ireland and was determined to play as a professional in the English Football League. However he was frequently told that he was too short to be taken on as an apprentice by an English club. However a late growth spurt saw him grow an extra six inches to reach the height of at age 17. By this time he also began playing for the Home Farm senior team in the League of Ireland B Division.