Coveny's senior club career spanned 20 years, mostly in Australia, with his most notable stint being at South Melbourne during their National Soccer League era.

The majority of Coveny's career was spent at South Melbourne in the NSL, and later on, Victorian Premier League.

Coveny, affectionately known by fans as Horsey due to his speed primarily played as a striker for South Melbourne.

Additionally, his goalscoring form in the OFC Championship in 1999 fired South to claim the title as Oceania's best and qualify them for the 2000 FIFA Club World Cup.

Here, Coveny would put in respectable performances including hitting the post twice against the treble winning Manchester United squad.

Following the disbanding of the back-to back winning squad, Coveny would stay at South and lead the new era in the new century.