For card tricks, see Make a Wish from Caleb Wiles's High Spots. I also do a variation of the Anniversary Waltz where the spectator's selected and signed card changes into a card with a birthday greeting on the face (either using a blank card with a message or a regular card that has a message appear). You could also play around with any spelling tricks, having the spectator spell "Happy Birthday to find their selected card. Or my personal favorite, card to birthday cake.
Diamond Jim Tyler has a pretty neat variation on Darwin Ortiz's 'Dream Card' mixed together with Card in Envelope called 'Birthday Card'. You can find it as a bonus on his 'Sweet!' DVD which can be seen here:
My presentation for it is along the lines of "If you could go anywhere around the world on your birthday, where would it be?" This is a great conversation starter to address to the spectator and opens up doors to a lot of potential by-play and banter. "That's interesting. Here i have a diary with hundreds of different places around the world. Please find your birthday and see the place next to it" The reason why I wouldn't do this trick on someone's birthday is because it can give the impression that the selection wasn't random. But either way, the trick is a nice way to mention someone's birthday in mid performance.
Finally, Wayne Dobson has a cool trick simply called Birthday Card which can be seen here: