Source - American censuses gave her Christian name. Al then found:
The films have arrived and your observation was correct, J Billingham and C Bradley were married by B J McQuaid, a priest in Madison, NJ. It now seems that James did marry catholic. I will note that his sister, Fanny, had been married by an Episcopal rector. Unfortunately, the official entry has no additional data about the couple, so I will need to discover where the original catholic parish records are kept.
By circumstance, I found that someone had ordered the microfilm of St
Patrick's RC Church, Newark - the church that James & Catherine would attend
as Catholics. (#1398552) Since it is quite long, I only have started and
found two baptisms for James & Catherine. The first is attached to this
e-mail and the second will follow. You will note that the mother is
Catherine Cunningham (not Bradley). I have written to the church where the
original marriage record, I think, exists and they have promised to respond
as their time permits.
I have a few notes to add about James Bellingham (b.c. 1822). I visited the
New Jersey archives and retrieved some data, but not anything with his
mother's name. My best hope for that name is the response from St Vincent
Martyr RC Church in Madison, NJ, where he and Catherine were married. By the
way, if he had never been baptized in the Catholic Church, would a priest
still marry them within the faith? I wonder if there might be a Catholic
baptism record for him with his parents' names. I did notice several adult
baptisms in the St Patrick's records that I sent to you. What I did find was
Catherine Bellingham's will in which she names her sons, James Bradley,
Thomas Bellingham and William Bellingham. So now I assume that her maiden
name was Cunningham and the she was a widow of a Mr. Bradley.