As far as I can tell no, there were false reports in 1993 that Serbia had received tactical nuclear weapons from corrupt soviet officials during the collapse of East German in 1990 but these came to nothing.

http://fas.org/news/serbia/931119-nuke.htm

While Serbia did have 40kg of highly enriched uranium at Belgrade the supporting nuclear power (and weapon) programmes had been abandoned in 1986 (after Chernobyl and with declining interest in a nuclear weapon). So if'd they decided to restart a nuclear weapons project it would have taken a while to start up.

Its this time delay that is probably why Serbia didn't start a nuclear project, it was seeking to provide a deterrent against European intervention (NATO would start bombing them in 1995). A nuclear bomb is only a deterrent when its built and deployable against your enemy so in the meantime Serbia would be still venerable in what was an on-going crisis. In any case the news of Serbia bomb programme (in violation of the Nuclear Non-Proliferation Treaty (NPT)) might actually increase European support for intervention.

Therefor it seems that Serbia didn't attempt to acquire nuclear weapons because while it had the capacity, it could not provide deterrence in the required timeframe and may in fact harm its strategic goals.

http://www.nti.org/learn/countries/former-yugoslavia/nuclear/