I can't give you a full answer but I do want to point out that Timor-Leste (East Timor) did not seek to seperate from Indonesia 'following' or as a result of Indonesia's independence (1949). Indonesia invaded and annexed Timor-Leste, a former Portuguese colony, following Portuguese withdrawal in 1975.
As someone else already noted, there is a significant contemporary and historic West Papuan independence movement. West Papua was also not part of Indonesia on independence in 1949, and continued to be held by the Dutch until 1961.
The South Maluku tried to proclaim it's own republic after the independence. The Netherlands has Maluku immigrants who still support their independent state. During the seventies the Maluku youth radicalised, there were violent actions such as two train hijackings.
Maybe a real historian can chime in, I am just a lurker on this subreddit.
The CIA, concerned by Indonesia's leftward tilt in the 50s, supported the twin rebellion of PRRI-Permesta, based in West Sumatra and Northeast Sulawesi respectively.
They leveraged regional resentment against growing Java-centrism in Indonesian government.
CIA aid included weapons, vehicles, planes, and personnel. Most notable was perhaps the downing and capture of US airman Allen Pope, who worked for the CIA.
In addition, several regions have seen an attempt to establish an Islamic state. In the 40s West Java had to contend with the Darul Islam rebellion, and more recently the Aceh region.
Not the fullest answer you're probably looking for, but there is a rather significant West Papuan independence movement