Coppin has appeared in the Melbourne Theatre Company's production of Born Yesterday, His Girl Friday, Ruby Moon, A Behanding in Spokane by Playwright Martin McDonagh, and as Vice Principal Panch in The 25th Annual Putnam County Spelling Bee, for which he wrote additional material.

Coppin is a fourth-generation Californian born in Roseville, California, the second child of Ronald and Gayle (Terry) Coppin. He was raised in the Sacramento suburbs of Rancho Cordova and Carmichael, California. The Coppin family are also long-term residents of Stinson Beach, California. Coppin attended Rio Americano High School and California State University, Sacramento before migrating to Australia aged 19, where he attended and graduated from the National Institute of Dramatic Art. He now divides his time between the United States and Australia after residing in Sydney for many years working in theatre, film and television. In 2001 Coppin moved to Melbourne with Jane Borghesi where the couple married in 2006. They have one son.

His many stage appearances include The Child Catcher in the Australian national production of Chitty Chitty Bang Bang, Mr Mushnik in the 2016 Australian national production of Little Shop of Horrors (musical), Robert Helpmann in his one-man play Lyrebird: Tales of Helpmann, and Puck in the acclaimed Opera Australia production of Benjamin Britten's A Midsummer Night's Dream directed by Baz Luhrmann with set and costumes by Catherine Martin. In 1989, at the request of Playwright Patrick White he played the role of the Young Man in the Sydney Theatre Company production of The Ham Funeral, directed by Neil Armfield.