I picked a day. For Cupid, it was February 14 (of course.)
That is what I do as well. I don't know Eddie's exact birth date. I know he was probably born sometime in October and I just picked October 31st.I usually just make up a birthday. If the dog is over a year old, I make their "gotcha" day their birthday. If they're puppies, I estimate what month they were born and just pick a random day that I will remember easily.