There is the 'Birthday' field in a personal account properties on the 'General' tab in PBA Provider Control Panel:
As Provider I want to ask the customer to fill it in the Online Store when registering a personal account.
Currently there is no such possibility. Adding birthday.tpl to be used on account information filling screen (inside co_accdata.tpl) does not work because of bug PBA-51156. Feature request PBA-50751 exists for Birthsday field to be added to Online Store.