First of all, you need to add an extra field to the users database, which will keep the birthday value. An example from our guide
on how to add a new extra field to users DB with the possibility to edit it on the Profile form contains all instructions.
Second, you will need to add this field to bb_cookie.php and assign it to some variable in the similar way as other login variables appear there.
At least, you will need to paste this variable in the template 'user_only_logged_in'.
Refer to our Premium service if you are in doubt on how to do it on your own.