Granted, there are a lot of perhapses in the above, but it doesn't seem like a conjunction of planets would worry people whose king had people on staff who could tell them what it was. But when the chumps are stumped, it's something else.
There are a couple of things in that gospel passage that are very intriguing, and probably give a strong indication about what exactly was happening at the time.
1. The point that Herod was troubled, and "all of Jerusalem" was troubled with him, sounds very odd -- since Herod was a pretty bad guy and I can't think of too many things that would disturb the people of Jerusalem as much as they would disturb Herod. Herod could possibly see a great leader in Israel as a potential threat, but that wouldn't bother the ordinary citizens of Jerusalem.
2. The gospel passage indicates that Herod and the people of Jerusalem became troubled AFTER the Magi explained exactly what motivated them to leave their homes in the East and travel to Jerusalem. So whatever it was that disturbed these people, it wasn't something blatantly obvious in the sky.
One other curious element of this is that Herod and all of Jerusalem were deeply troubled by something that the Magi had assumed to be a wonderful, world-changing event. So whatever it was that troubled Herod and the people of Jerusalem had to be something that the Magi didn't understand, or didn't consider all that important.
The combination of these factors tells me that what the Magi saw in the sky prompted fear in Herod and the citizens of Jerusalem over the one thing that would have affected them greatly but would not have affected the Magi very much at all -- the Roman forces occupying Israel at the time. Herod wasn't troubled because this great leader of Israel represented a threat to him -- he was troubled because the interpretation of events in the night sky described to him by the Magi would likely have been interpreted in a similar manner by the astrologers in Rome. If the emperor of Rome had been told by his astrologers about an omen in the sky indicating the birth of a great leader in Israel, then Herod and all of the people of Israel would have much to fear.
The events in the night sky that would be interpreted in this way would have to meet a couple of different criteria, and anyone who has the ability to research these things might pursue this further:
1. It had to be something in the sky that looked "normal" to most people at the time, so I've ruled out a comet or supernova and would focus on planetary activity (which was often studied among wise men in different cultures back then).
2. It had to be something that didn't occur very frequently, since many celestial events like planetary conjunctions occur at multiple times over the course of many years -- and this one had to be so different than the others that it prompted the Magi to travel from the East.
3. It had to occur over a period of time, since it was evident in the sky at different points in time as the Magi traveled from the East. Also, Herod's fixation on when the "star" first appeared -- and his subsequent order to have every male child under the age of two killed -- indicates that this series of events occurred over at least a 1-2 year period.
4. It had to have some relevance to Israel, which could mean planetary activity in the constellation of Aries (because the Ram was seen as the symbol of Israel at the time) or Leo (because of the Old Testament references to Judea in the context of "the Lion of Israel").
5. It also had to have some importance to the Romans, which would lean toward something related to Mars (the Roman god of war) or Jupiter (the head of all Roman gods).
Based on these factors, I'd go back to a ten-year period leading up to 0 AD and see what happened in the skies involving Mars and/or Jupiter and the constellations of Aries and/or Leo over a 1-2 year interval.