The club started well by winning the FAI Junior Cup in their first season, beating Grangegorman in the final at the Showgrounds 3–0. The following season also brought silverware in the shape of the Connacht Junior Cup with Rovers beating Galway in the final 1–0 after a replay. At the beginning of the 1931–32 season the club successfully applied to join the Dublin-based Sunday Alliance League and won their first game at this level by beating Windy Arbour 4–2 at the Showgrounds and went on to win the league, finishing four points ahead of Westland Sligo. After this success the club moved up another level the following season by joining the Leinster Senior League and played their first game away to UCD in August 1932 and won 4–2. The club performed well in their first season at this level eventually finishing third as Brideville won the league. This season also saw The Bit O' Red make their first appearance in the FAI Cup, winning in the First round against Brideville 3–1 before going out to Shelbourne in the next round 5–2. The next year, the club won the Leinster Senior League in only their second year at this level by beating Distillery in a play-off at Tolka Park 3–2 after the teams had finished the league level on points. The team also won the Intermediate Cup, winning 5–1 against Waterford side Tramore Rookies in the final at Dalymount Park, as well as the Metropolitan Cup, beating Queens Park 3–0 in the final at Tolka Park to secure a remarkable treble for the young club.