Well, when I don't know the date they are born, I just make their birthday the 1st of the month going about 6-8 weeks back. So I've had lots of cats celebrating a birthday on the 1st of a month.
Now Noa came here early June, but I thought April 1st was not nice, so she has March 31st
Must say I had to change this system, as my son likes to give them a birthday close to his own if possible.