I was just reading a borrowed Christian magazine that had a great article in it on this subject, but it only gave a clue to the date.
This article pointed out that Zacharias was the priest, and named the order. If you go back into the Old Testament, you can find out what dates that each priest was to be 'on duty'. They were assigned a week at a time, twice a year.
From there you should be able to get an idea of when John the Baptist was born...and from there about the time that Jesus was born.
Luk 1:5 ¶ There was in the days of Herod, the king of Judaea, a certain priest named Zacharias, of the course of Abia: and his wife [was] of the daughters of Aaron, and her name [was] Elisabeth.
Abia in the OT is Abijah. At some point in, I believe 2 Chron. David appointed what order of priest was to serve during specific times. I am going to do some research on it, however math is not my strength. Does anybody have any info on this?