I've read in thegrandline.com about the Straw Hat's birthdays. Zoro, Nami, Sanji and Robin's b-day are based on the play on their names. Take note that they are the four that are the good looking ones among the SH. Luffy, Usopp, and Chopper's b-day are based from Children's Day, April Fool's and Christmas respectively and they are the one that are the freaky ones.
Since Franky is a freak. His b-day could be also based from a holiday or a festival. These are some holidays that I could think of that can become his b-day.
Labor's Day (May 1)- maybe because Franky is a worker??
Halloween (October 31)- Franky w/ mask? Cyborg-Frankenstein-Centaur = Scary
No Pants Day (1st Friday of May)- cause he doesn't wear one
Father's Day- he could be the Straw Hat's father figure
I couldn't think of any other thing now. Now, what other holidays could be Franky's b-day?