Coia was born in Wolverhampton but grew up in Glasgow. After obtaining a diploma from Glasgow School of Architecture in 1923 he joined the architectural firm of Gillespie, Kidd, and Coia. In the 1930s a series of commissions for Roman Catholic churches cemented Coia's reputation. As the son of an enemy alien, Coia was left vulnerable by the outbreak of war with fascist Italy. He closed his office in 1941, having been elected a fellow of the Royal Institute of British Architects. Coia reopened his office in 1945 and resumed designing churches for the archdiocese of Glasgow. Most of these post-war buildings, however, were severely constrained by limited budgets. During the 1950s Coia's architectural practice expanded and he became a key public figure in Scotland.