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According to the New Jersey State Archives, births prior to 1848 were not filed at any governmental level (town, county, state). The only exception is the Records of Births of Slave Children that were filed with the county clerks beginning in 1804. See Genealogical Records at the New Jersey State Archives for more information.
It looks like church records are your best bet. If you have an idea of when and where they got married, you could check out the church records and hope that the marriage information includes parents in it as well.