Setting custom reminders for birthdays in ios calendar
Settings > Mail, contacts, calendars > Default alert times > birthdays

Apparently there are a few options here. You cannot specifically set a custom time at the time of my writing this, but it is possible to pick "a day before", "2 days before", "1 week before" or on day of event. I don't see a way to select a different time though other than 9 am.