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Have you tried familysearch.org...it is a free website, you just need to join to search. You might find their marrieage date there. or you could try Ancestry.com..they give a two week free trial.
Good Luck..hope you find it
Dear Ms. Atkinson,
Thank you for posting your question on the History Hub!
If he married while in the Navy, there might be information in his Official Military Personnel File (OMPF). Therefore, we suggest that you request a copy of his OMPF. OMPFs and medical records of enlisted men and officers of the U.S. Navy who were separated from the service after 1957 and prior to January 31, 1994 are located at NARA's National Personnel Records Center (NPRC), (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. To request these records, please mail a completed GSA Standard Form 180 to NPRC. You also may fax the form to 314-801-9195. Veterans and their next of kin also may use eVetRecs to request records. See eVetRecs Help for instructions. Certain information in the records is not available to the general public without the written consent of the veteran or his next of kin. For more information see Request Military Service Records. For a complete copy of a personnel file, in Section II, on the line for "Other" (Specify), write "Complete copy of every page of personnel file - not an extract."
Due to the COVID-19 pandemic, the NPRC was closed from March 23 through June 23, 2020. As of June 24th, the NPRC entered into Phase One of a gradual reopening process. The center is currently only servicing emergency requests and will soon expand its service to include time-sensitive requests from veterans for records needed to secure VA home loan guarantees and employment opportunities. We apologize for any inconvenience.
If they were married while living in Alabama, please request a copy of the marriage certificate from the Alabama Department of Health.
We hope this is helpful. Best of luck with your family research!