Most date pickers assume that the date is in the near future and that the "day of week" context (ie: tuesday) is useful to the user is selecting the date.
Birthdays are the opposite. They are typically decades in the past, the user doesn't know or care what day of the week they are, and the user knows the numerical date by heart.
The only things I've come up with are:
1) Text entry that attempts to accept different formats and displays the formatted parse of the format next to it. Decent on desktop, text entry on mobile is poor.
2) Big array of Years / Month / Day buttons. The possible range of years is limited (nobody alive was born in year 1200) to a little over 100, so this does scale. User simply needs to tap on the correct button 3 times, which is nice, but the picker takes up sooo much visual space.