Is there a way to edit contacts birthdays on the phone? As far as I can tell the default contacts app on the phone does not have a field to enter or edit birthdays. 

Is there a way to do this?

What about other contact apps?
On my phone, I can't enter contact's birthdays, but if I've previously entered their birthday on GMail then it does appear in their Contacts entry on the phone, and I can edit it there. Not that useful, as the birthday field is something you're likely to add to someone, and then its not very likely to ever change after that!

One workaround that I use if I'm entering this on the phone is to add their birthday into the Notes field, and then later on when I'm at a PC I can go into GMail and put the birthday in properly.

This is using the Contacts app on a Galaxy S using their stock Froyo  (2.2.1).