Thank you for posting your question on History Hub!
Beginning September 27, 1906, the responsibility for naturalization proceedings was transferred to the Federal courts. It took time for the lower courts to let go of the practice, so researchers may need to look at lower courts if the National Archives does not maintain a record of naturalization from the early-mid 20th century. Records from state and local courts are often at state archives or county historical societies. It could be the reason that you have not been able to find anything yet is because your relative was naturalized at a State or local court.
To better help in identifying where your relative was living, so as to possibly help to identify the court where he could have been naturalized, we would recommend that you try to find your relative in Census Records. Ancestry and FamilySearch can be helpful tools for searching Census Records.
If a naturalization took place in a Federal court, naturalization indexes, declarations of intention (with any accompanying certificates of arrival), and petitions for naturalization will usually be in the National Archives facility serving the state in which the Federal court is located. No central index exists. To ensure a successful request with the National Archives researchers should include: the name of petitioner (including known variants); date of birth; approximate date of entry to the US; approximate date of naturalization; where the individual was residing at the time of naturalization (city/county/state); and country of origin.
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 RW-SB. We apologize for this inconvenience and appreciate your understanding and patience.
In most cases, the National Archives will not have a copy of the certificate of citizenship. Two copies of the certificate were created – one given to the petitioner as proof of citizenship, and one forwarded to the Immigration and Naturalization Service (INS).
Certificates of citizenship were issued by the Federal courts until October 1991 when INS took over responsibility for naturalization proceedings. All INS records are now overseen by the US Citizenship and Immigration Services (USCIS). USCIS maintains duplicate copies of court records (including the certificate of citizenship) created since September 27, 1906 and may be requested through the USCIS Genealogy Program.
For more information you may wish to visit - https://www.archives.gov/research/immigration/naturalization
We hope this information is helpful and best of luck with your research!