Thank you for your inquiry about this. At this time you can only associate one email address per contact. This includes any primary contact fields such as first name, last name, and birthday. As you mentioned, you could update the birthday field after the first one goes out but this is a manual process and you would have to change it back and forth after reach one. I can understand how that might be a cumbersome process. If it's possible for one of the two contacts to provide an alternate email address then you could create a new contact with all the relevant information.
I will be passing your inquiry to our developers as feedback about being able to include multiple names and birthday information to an individual contact. I apologize for any inconvenience!
Thank you for checking on this issue! We do have a feature request for this still, though there hasn't been any additional workarounds. If you also are in need of only two dates, you could treat one of the birthdays as the 'anniversary' date, but that birthdays and anniversaries are still the only two fields that can store that kind of information and trigger autoresponders. I'll add you to the list of people requesting this feature as well.