We leave birthdate blank, in line with instructions received from the IRS at 1-800-800-2877. I don't think alphabetical characters such as "N/A" logically belong in a field where sensical responses would involve only numbers.
We e-file now, and when we asked a similar question of the E-filing system handlers (actually we were asking how to indicate "unknown" on SAR suspect fields, where we have a name and address, but no phone number, date of birth, or TIN), they responded that if it is a numerical-only field such as date of birth, phone number, zip code, SSN, etc, which disallow alphabetical characters (in the e-filing system), then the fields should be left blank.
"It is natural to give a clear view of the world after accepting the idea that it must be clear." - Albert Camus