At senior club level, Kirkwood played for Queen's University, Belfast YMCA and Lisnagarvey. During his club career he won ten Irish Senior Cup winners medals. He won his first with Queen's in 1981 and his second with Belfast YMCA in 1985. Then between 1987–88 and 1993–94 he was an ever-present in the Lisnagarvey team that won the cup for seven successive seasons. He won his tenth medal when Lisnagarvey won the cup in 1996–97.
