Coulter was a member of the St Joseph's Boys FC in Sallynoggin, where he played all through the underage structure before signing with Dundalk F.C.
U-20 side in 2008 [1][2] He made his debut in the League of Ireland Premier Division on 10 April 2009, starting in the home match against Bray Wanderers, which finished as a 1–1 draw.
[9] He broke a long standing clean sheet record in the Atlantic Sun Conference set by Jeff Cassar.
[16] On 20 February 2019, Coulter joined Forward Madison FC in USL League One as a player-coach for the team's inaugural season.
[21] Coulter joined USL Championship side Rio Grande Valley FC in March 2020, serving as a player and the club's goalkeeping coach.