In the 2009–10 Celtic League, Muldoon played 14 games for Connacht, starting in each of them as the province finished bottom of the table for a third successive year. Connacht performed far better in Europe however, and topped their pool comfortably, winning all six games with two try bonus points. The team proceeded to the quarter-finals as the competition's top seeds. In the quarters, they faced the French Top 14 side Bourjoin, beating them 23–20 with a late Miah Nikora drop goal. Connacht advanced to the semi-finals where, on 30 April 2010, they faced a Toulon team featuring the English fly-half Jonny Wilkinson. Toulon won 19–12 in Galway, with Wilkinson kicking 14 of the French club's points. Muldoon played in and started all but one of the team's games, not playing in the home match with Olympus Madrid. He scored three tries in the competition, crossing the line against Madrid, Bourjoin and Worcester Warriors.