Conque played collegiately at Southwest Mississippi Community College and then Nicholls State University where he was named first-team Associated Press All-American in 1982.

[1] Conque began his college coaching career as a graduate assistant at his alma mater, Nicholls State University in 1984.

[4][5] Conque was head football coach at the University of Central Arkansas from 2000 to 2013, compiling a record of 105 wins and 59 losses.

Conque was 5-3 in Southland Conference games, including wins over sixth-ranked McNeese State and eighth-ranked Southeastern Louisiana, finishing tied for third.

[10] Conque announced his resignation on August 6, 2018 stating “Although I have remained confident in the ongoing investigation into the potential violation of university policy, as a family of faith and out of respect to my profession, I do not want this situation to be a further distraction to the 2018 football team and season.