Born in Salzburg, Kuljić started his professional career in Salzburg but made his name at Austrian Football First League side SV Pasching with whom he won promotion to the Austrian Football Bundesliga in 2002. He repeated that feat with SV Ried in 2005, when he also became 2nd division top goalscorer. In 2006, he became league top goalscorer and subsequently moved abroad to join Swiss side FC Sion but controversially returned to Austria after one year when he signed for Vienna club Austria Wien.