Conroy began his career with Coventry City in 1983. Unable to break into the first team, he moved back to his native Scotland in 1984 to sign with Clydebank on a free transfer. In three years with the Bankies, he made 114 league appearances and scored 38 goals.
In 1987 he joined St. Mirren for ten months, scoring one goal in ten appearances for the Buddies.
He returned south of the border in 1988 to join Reading in a £50,000 deal. He spent three years at Elm Park, before moving to Burnley in 1991, where the most prolific scoring period of his career would begin.
In his two years with Burnley, Conroy scored 30 goals in 77 league appearances.
Conroy joined Burnley's Lancashire rivals Preston North End in 1993 for £85,000. He went on to score 22 goals in 57 appearances for North End and briefly played alongside a young David Beckham.
In 1995 he joined Fulham, and scored 32 goals in almost 100 appearances for the Craven Cottage club.
After three years in London, Conroy moved back to Lancashire to join Blackpool for a £50,000 fee. He made fourteen appearances for the Seasiders but failed to find the net. In December 1998 he was loaned out to Chester City, for whom he scored three goals in ten appearances. He returned to the Blues, again on loan, a month after his first period expired.
After leaving Blackpool in 1999, Conroy moved to Australia to play for Carlton.
In 2000 he joined Eastern Pride, with whom he finished his playing career when they went out of business the following year.
Conroy is currently the senior coach at Doncaster Rovers Soccer Club in the Victorian State League Division 2. He began his coaching career as reserve-team coach at Doncaster Rovers.