Career
He also previously played for Dundee United, Clyde (on loan) Dundee, Forfar Athletic, Carnoustie Panmure, East Fife, Livingston and Peterhead. Born in Dundee, Conway started his career with hometown club Dundee United but made just two substitute appearances for the Terrors, appearing in games late in each of the 2002-2003 and 2003-2004 seasons. Conway played ten games during a loan spell with Clyde, scoring his first senior goal, before being released from Tannadice in January 2005.
On Wednesday 30 June 2010 Conway signed for newly promoted Second Division side Livingston, from East Fife, on a deal which would keep him at Almondvale for 1 season.;
On 3 June 2011, Conway left Livingston to join Peterhead.
After leaving Peterhead in 2013, Conway signed for Highland Football League side Buckie Thistle.