Coyne's earliest performances were in school plays. He played leading roles in two outstanding productions: ‘The Judge’ in Oscar Wilde's 'Hang of the Gaol' and 'Phaeton' in Ovid's Chariot of the Sun. He won rave reviews for his performances in the national press and decided to pursue a career as an actor.He won a place at the Royal Academy of Dramatic Art in London and upon his graduation, he received the Hannam Clarke Award.
His first role on TV was on an episode of London's Burning in 1990. His next big role was in a mini-series Gulliver's Travels starring Ted Danson. He appeared in many British TV series over the next few years including guest appearance on EastEnders, Pulling and The Bill. In 2003, he was cast in Lara Croft Tomb Raider: The Cradle of Life. In 2010, he was cast in The Nutcracker in 3D.
His biggest role was as Warden Edwin James on Alcatraz. He was later cast in Would You Rather and the British film, London Boulevard. In 2013, he was cast in two major films, in a supporting yet adequate role. He was cast as a henchman in Gangster Squad and as the right hand man of John Goodman's character in The Hangover Part III.