It's not the easiest thing to follow, but http://bethlehemstar.net has a very interesting hypothesis on the subject. The information is all there, especially in footnotes, but unfortunately it's not presented very clearly on the site itself... they want you to get the video.* The upshot is that the date is most likely 3BC, and maybe 2BC.
You get around the Herod problem because of a recent study that found a typesetting error made in 1544 for the manuscripts used to date Herod's death. It is now believed he died in 1BC, rather than 4BC:
The Bible recounts that Herod learned of the Messiah's birth from astronomers who had seen the Star of Bethlehem. He tried to kill the child, so, obviously, the Bible records that Herod was alive at Jesus' birth. Remember that this mattered to Kepler, because historians of his time apparently inferred from Josephus' history that Herod died in 4 BC (9). Necessarily, Kepler assumed Christ was born before that date, perhaps 5 BC or earlier...
But modern scholarship has deepened our understanding of Josephus' manuscripts. A recent study was made of the earliest manuscripts of Josephus' writings held by the British Library in London, and the American Library of Congress. It revealed a surprise that allows us to target our mathematical telescopes better than could Kepler (10). It turns out that a ... printer typesetting the manuscript of Josephus' Antiquities messed up in the year 1544. Every single Josephus manuscript in these libraries dating from before 1544 supports the inference that Herod passed in 1 BC. Strong recent scholarship confirms that date (11).
* As a side note, the video is well worth your time. It's just a shame that they charge for it; this is something that would be good to see spread more widely.