Woodhouse entry for birthday:
Birthday, > used as adj. P. and V. [size=150]γενέθλιος[/size]. Birthday offerings to the gods : P. and V. [size=150]γενέθλια, τά[/size]. Hold birthday sacrifice : P. and V. [size=150]γενέθλια θύειν[/size].
Seems that their birthday was a day for sacrifice. 
Now, what did greeks say in their friends’ birthday to celebrate it? What was their equivalent to “Happy birthday!”?