There has not been any attempt but it was mainly because Romania's first elected president stripped the King of his citizenship and barred him entry into the country. Michael was turned back at the airport when he arrived in the country during 1990 and at the time he was immensely popular. If an attempt to restore the monarchy would have happened then, I'm pretty sure it would have happened. Nevertheless, right now support is around 30% if I remember correctly, the King is extremely old and ill and in no position to assume the throne anymore. His daughter, Margareta has a very unpopular husband and is not very popular herself either. Chances of a restoration in Romania are close to 0. I'm a republican myself, but I do think the country could benefit from a more socially active royal house.
Yeah, that more or less fits what I've read about Iliescu. A real bastard that guy was, it's a shame you guys got screwed over like this. "The worst thing about communism is not communism itself but what comes after it's gone." —Adam Michnik.
In Poland, the conditions for monarchy restoration were much more favorable in the '90s but Poland had been without a Polish-blooded king at least for the past 200 years and the dude next in line was German (so you can imagine the lack of popular enthusiasm). Besides, the country's been a republic since 1918 and even under monarchy it had been pretty damn republican in its character so there wasn't much need for that.