Ancient sources cite the 10th day of the month of Gamelion as the day of Epicurus' birth.  As such, he held a feast in his Garden, and later when his hero cult evolved he was celebrated on that day.

The month of Gamelion is the month of marriage (gamos), situated in the latter part of January and the early part of February.  It doesn't fit exactly into our calendar because the Attic calendar in use in ancient Athens was lunar, not solar.  

Modern Epicureans have two options to establish a day for celebrating Epicureanism: one would be to stick to the 10th day of Gamelion and count ten days from the January new moon, which is a bit archaic in my view and opinion.

The more practical option is to choose either January 10th or some day in mid January as a day for outreach and education on the legacy of Epicurus.  Maybe when there are more Epicureans on the forum, we may be able to have a vote on what is the best way to fix a date for Epicurus' birthday in our calendar: I think it would help to generate awareness of his legacy and more visibility for humanism in general.