The only real evidence I can find of any internal attempts to change borders prior to the late 80s/ early 90s was the Nazi and Fascist Italy attempting to "persuade" Croatia to become independent, to push for more autonomy so to speak. When Yugoslavia as a whole was invaded by Axis powers in 1941, Croatia was given independence from Yugoslavia by the Nazis, who then encouraged the Croatians to participate in the killing of Serbs within its borders (these killings seem to be more motivated by religious rivalries as opposed to nationalist or ethnic motives). It was throughout this war that the Chetniks (Royalists determined to see the re-establishment of a monarchy) and the Partisans (communists) fought for control of Yugoslavia from the Axis powers (led by Nazi Germany). During this war, Josip Broz Tito distinguished himself when he led the Partisans to victory over both the Axis powers and the Chetniks. He had a dedicated following, dedicated enough that when the war came to an end, it was decided that the exiled monarch (King Peter II, the last King of Yugoslavia) would stay in exile. Tito also received aid from the Soviets during this war, and the Soviets also helped him set up the Socialist Federal Republic of Yugoslavia in 1945. I'm harping on about Tito here because of the defining role he played in keeping Yugoslavia together during his reign as President. Tito modeled his secret police on the Soviet KGB, they acted in a manner similar to the KGB, often extrajudicially and almost always omnipresent. Tito used his secret police to crack down on any feelings of nationalism, purging any and all growth of nationalism. The suppression of nationalistic feelings and an odd mix of deference and repression is what held Yugoslavia together during Tito's reign. Tito allowed all ethnic groups to speak their own language. Eg; Croatians could speak Croatian and Serbians could speak Serbian and so on. However, in relation to Albanians, Tito took an incredibly harsh stance, arresting and imprisoning many Albanians for expressing their ethnic identity. According to Matas, almost half of the political prisoners in Yugoslavia were Albanians. This is significant because Matas also asserts that Yugoslavia had more political prisoners outside the USSR than the rest of Europe combined.

I may have gone on a bit long about the role of Tito but that's because he was instrumental in keeping Yugoslavia together. When he died in 1980, the Presidency became decentralised and the country was held together by the ideological force of Communism. It was when communism collapsed in 1989 (with the Fall of the Berlin Wall etc.) that Yugoslavia lost its unifying factor and ethnic tensions began to rise.

Edit: In my studies on this, I haven't found any evidence of attempts to change internal borders during Tito's rule

Resources: Matas, David (1994). No More: The Battle Against Human Rights Violations. ISBN 1-55002-221-0. Finlan, Alastair (2004). The Collapse of Yugoslavia 1991–1999. New York, USA: Osprey Publishing. ISBN 978-1-4728-1027-4. Corbel, Josef (1951). Tito's Communism. Denver, Colorado: The University of Denver Press.