This may seem a bit simple, but I wonder if you have considered how a birthday list can help you with your family tree?
Start with a sheet of paper or preferably a new document on your computer. The computer makes it so much easier to correct mistakes and to reorder things in case you get a date wrong.
Start with your name and birth date. Easy enough. Then work sideways, then backwards. By sideways, I mean list the names of siblings and their birth dates. Then list your parents and THEIR siblings. If you know an exact date, list it (i.e. - 10 May 1948). If you're not sure, record what you think and include a question mark (i.e. - 10/11 May 1948 or 10 May 1948/49 or May/June 1948). You can also use abbreviations commonly used when dealing with dates in family history - ABT for About, BEF for Before, AFT for After. So, if you know a cousin was born before your, but you're not sure when, you can record the date as BEF 1950 (assuming your year of birth is 1950 in this example).
Once you have this list, identify two or three people on the list with birthdays in the next month or two. Send them each a card a few days early when the day comes, even if it has been several years since you last had contact. As part of your message, let them know you've been thinking about your extended family and are beginning to work on your family tree. They will certainly be in touch with other family members on their birthday and will likely mention your surprise card to others. Word will travel that you're working on the family tree.
Be sure to include your current mailing address, phone number, and an email address if you have one. If you use Facebook, you can also let them know to seek you out there as well. If the person you're contacting may not immediately know who you are, then be sure to introduce yourself and include a little detail explaining how you are related.
I've never met a person who didn't enjoy getting a surprise birthday card in the mail!