Konnafis was born on August 28, 1979 in Nicosia. He started his top-league career with Omonia in 1996. In 2002, he transferred to Anorthosis Famagusta. He had a one-year stint in the Belgian League with Gent (2004) before returning to Cyprus to play once more for Omonia. In 2007, he moved on to Apollon Limassol.
Konnafis was capped 25 times by the Cyprus National Football Team.