If you are looking for the birth of someone whose parent(s) were US citizens and were out of the country at the time of the birth of their child, Ancestry.com ( paid research site) has US Consular Reports of Births 1910-1949, which were taken from Record Group 59 (State Department) records at NARA in College Park MD.
If you are looking for the birth record of a person who became a naturalized US citizen, that record would be in the country where the person was born, although there may be a copy of the record in their naturalization file.
Thank you very much for taking the time to answer my question and reference to College Park. A researcher in Boston has helped with this, but she found that the particular volume we need was apparently not digitised (Vol 337 1920 Jul - 1920 Sep). I have sent an email to College Park, but wonder if Ancestry would also be able to shed some light on why this volume is missing?
Sounds like your luck is about the same as mine when it comes to research. The following is from the description of the records on Ancestry.com, where they reference one missing volume:
Many of these reports were received with other papers and correspondence, you may want to look at previous and subsequent images to find all the information pertinent to a specific individual. There are some records that were not found at the time this data was scanned. Currently missing from this collection are 1 bound volume, containing approximately 400 records, as well as three boxes of loose paper (boxes 363, 364, and 365) containing records for the surnames Canwell through Colom.
Many thanks Susannah
Dear Mr. Teale,
Thank you for posting your request on History Hub!
The database that you have already checked on Ancestry is derived from the National Archives record series Decimal Files, 1910 - 1949 in the General Records of the Department of State (Record Group 59). Unfortunately, as has already been said, some of the records that should have been in that series are missing. Also, in 1920 there was no legal requirement to report a birth to the consulate, therefore, in many cases parents may not have done so. There is a miniscule possibility that there are relevant records in the files of the individual consulates or embassies that were not included in the the Decimal Files series, however it must be emphasized that this would be an extremely exceptional circumstance. For more information, please email the National Archives at College Park - Textual Reference (RDT2) at Archives2reference@nara.gov and provide as much information as possible about when and where the birth you are researching took place.
Due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from RDT2. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this is helpful. Best of luck with your research!