Cooley settled in Dublin after winning first prize in a competition organised by the city to build a Royal Exchange. This was built and later became City Hall. It is believed that he studied in London, and was a pupil of Robert Mylne who built Blackfriars Bridge over the Thames. In 1775 he was appointed chief architect to the Board of Works. He designed Newgate Gaol in Dublin, and designed several buildings in Armagh including the Archbishop’s Palace, the Library and the Royal School. He designed several country houses also: Caledon, Co Armagh in 1770 and Mount Kennedy Co. Wicklow. Prior to his death, he designed a Public Records Office which was incorporated by James Gandon into his Four Courts.