Special Collections and Archives is the repository for the records of a number of churches and religious bodies. These are described in:
A Guide to Original and Copied Records of Religious Organizations, Largely New Jersey Churches, in the Special Collections and University Archives of Rutgers University. Donald A. Sinclair. New Brunswick, N.J. : Genealogical Society of New Jersey, 1999. Available?
The New Jersey Historical Society has church/religious body records in it's collections.
The Jewish Historical Society houses the records of a number of synagogues in the MetroWest area (Essex, Morris, Sussex, and portions of northern Union counties). Click on "Archives" and then "Finding Aids" to see lists of available collections.
Synagogue Records and Related Materials
Arranged by county.