There seems to be consistency for these birthdays. My old 1999 calendar also says that June 1st is Oscar's birthday. The birthdays this month, according to my old calendar, has The Amazing Mumford's birthday on June 7th and Maria's birthday on June 26 (I'm not sure if the human characters' birthdays are the same as the actors' actual birthdays).
I saved this calendar because it is a real cool one with pictures of the muppets and live animals.