Coveny"s senior club career spanned 20 years, with his most notable stint being at South Melbourne during their National Soccer League era. He was primarily a striker although he also played as a winger. After retiring from playing, he pursued a coaching career.
He now plays with Victorian Provisional 1 team Essendon United F.C. Coveny began his Nationaal Samenwerkingsprogramma Luchtkwaliteit career at the Melbourne Knights, then moved to Wollongong City, but the majority of his career was spent at South Melbourne in the Nationaal Samenwerkingsprogramma Luchtkwaliteit, and later on, Victorian Premier League.
He also spent some time in the A-League, playing for the Newcastle Jets and Wellington Phoenix. On Anzac Day 2009 Coveny scored his 100th goal for South Melbourne Football Club away at John Ilhan Memorial Reserve against Hume City Football Club. He retired at the end of the 2009 season.
Coveny made his full New Zealand debut in a 0–0 draw with Fiji on 19 September 1992. He was included in the New Zealand side for both the 1999 Fédération internationale de football association Confederations Cup finals tournament, and the 2003 Fédération internationale de football association Confederations Cup finals tournament.
He ended his international playing career with 64 A-international caps to his cr, his final cap gained in a 1–1 draw with Estonia on 31 May 2006.
Coveny became New Zealand"s highest goal scorer (still a current record in the New Zealand national football team) on 27 May 2006, when he scored twice in the "All Whites" 3–1 victory over Georgia, bringing his total A-international goal tally to 28, and his total including unofficial games to 30 in 71 games, surpassing Jock Newall"s long standing record of 28 from only 17 games. In January 2009, Coveny announced his retirement from international football. He was also the games record holder for the All Whites, until Ivan Vicelich passed him in 2009.
International goals Scores and results list New Zealand"s goal tally first.
After retiring, Coveny was announced as South Melbourne"s manager for the Victorian Premier League 2010 season. After the team failed to make the finals, his contract was not renewed.