[citation needed] Most of Rivaldo Costa's successes in football come from his time in Asia, most notably in Indonesia, where he played for Petrokimia Putra Gresik and Arema Malang in 2003 and 2004 respectively.
However, Gresik were knocked out by eventual winners East Bengal FC in the Semi-Final, but in the Third Place Match on July 26, Rivaldo Costa scored first to help his team to a 3–0 win over Perak FA.
A year later, Rivaldo Costa picked up his first major medal, scoring 12 goals as he helped Arema Malang to the Indonesian Division 1 (Divisi Satu) title, but it was a short-lived stay at the club, as he returned to Brazil to play for Bonsucesso in Rio de Janeiro.
On May 20, 2008, Rivaldo Costa scored his first goal for Geylang a decisive equaliser in the 94th minute to grab one point in a nail-biting 2–2 draw against Balestier Khalsa.
Rivaldo Costa and his compatriot Luiz Carlos Machado Júnior have been released from Geylang United following an unsuccessful 2008 season where they finished 6th in the league.