Coyne, who is the son of former Brisbane City NSL player and Australian International John Coyne and older brother of Jamie Coyne of Perth Glory, started his career with Australia side Perth S.C. before a £20 000 move to England with West Ham United in January 1996, where he was part of the West Ham youth team that reached the in 1996. After loan spells at Brentford and Southend and one appearance for West Ham against Leeds United, Coyne moved to Scottish Premier League club Dundee on a free transfer in March 2000. He made his debut for Dundee in August 2000, and made 28 appearances in all competitions during the 2000–01 season. Manager Joe Kinnear described him as "22 old, six-foot two, an Australian international ... big and strong and uncompromising. He can pass with both feet. He reads it well, and he's young enough to improve." He scored an own goal on his debut for Luton against Lincoln City in September 2001, but successfully established himself in the first team, making 31 appearances in that season, despite suffering a knee ligament in December 2001 that sidelined him for several weeks, and helping Luton to set a club record of winning twelve successive games and to promotion to Division Two.