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The National Archives at New York City holds naturalization records - specifically Declarations of Intent and Petitions for Naturalization - for naturalizations done through the federal courts in New Jersey. You can contact that office directly by emailing firstname.lastname@example.org
When requesting a search, please provide the full name of the person and, if known, their date of birth, the city/state they were living at the time of naturalization, date they naturalized, and spouse's name, if they had one. All of this information helps to narrow the search and to confirm the correct record has been found. Once the record is located, the staff will provide you with information about the record and instructions on ordering copies.