The priests were divided into 24 courses. 1Chronicles 24:10 indicates Abijah (Zechariah's division) was the 8th. There is also an extra-biblical quote from a Jewish source indicating that each division would serve for one week.

“Moses, our master, divided the priests into eight courses, four from Eleazar, and four from Ithamar, and so they were until Samuel the prophet; and in the days of Samuel, he and David, the king, divided them into twenty four courses; and over every course one head was appointed, and they went up to Jerusalem to the service of the course every week; and from sabbath to sabbath they changed; one course went out, and another came in, till they finished, and returned again.”

There's a nice web page based on these ideas and concludes that Jesus was conceived on Dec 15 (the Jewish festival of lights, or Hanukkah), and was born on the Feast of Tabernacles Tishri 15 (between September and October)
http://www.aloha.net/~mikesch/sukkoth.htm

Another supporting evidence is the hypothesis that the reason why there was "no room at the inn" in Bethlehem was because there was a big feast going on in the nearby city of Jerusalem. That may or may not have been the case. It could have been that there was no room simply because of the census. But if it was because of a feast, there were three annual feasts in which all males were required to travel to Jerusalem - Passover (Nisan 14-21), Pentecost (Sivan 6) and Tabernacles (Tishri 15-22). However the problem with the Tabernacles idea is that the celebration of Tabernacles required the people to not stay at inns, but rather to live in booths (tents) Leviticus 23:42. So it seems that there should have been plenty of room at the inn.

However what the author failed to consider was that Zechariah's division would have been serving twice a year. The second assumption therefore is that Zechariah served the first of these two terms. But if he served the second term, that would have been about six months later, which would shift everything by 6 months. Jesus would have then have been conceived about June 15th and born about March 15th (only approximate dates). Interesting that March 15th is very close to Passover, which is one of the big celebrations in Jerusalem. And wouldn't it be interesting if he was born on Passover and died on Passover! Or possibly that Passover was 8 days after his birth, at which time he got circumcised, which involved shedding of blood, and of course his death at passover also involved the shedding of blood. And that would perhaps allegorically connect his entry into the world itself to his triumphal entry into Jerusalem which occurred about a week before his death.

But still a Dec 25th birth is not out of the question either, as we have had to make a couple of assumptions to come up with these two other possibilities. See also http://www.wcg.org/lit/jesus/datebirth.htm for other possibilities.

There may be also other evidences to consider such as the shepherds attending their flocks outside at night. One might think that it would be too cold to do so in December. And then there's the star of Bethlehem. But there's even more a variety of speculation as to what it was and whether it narrows the time frame or not.