Unfortunately, I think you may have to check around where they lived for the local church that was in service at the time. NYC didn't require marriage records until around 1881. Same with birth records. I was able to track down the church for my 2nd great grandparents and obtained all the baptismal records but like you, I am still searching for that elusive marriage record.
Looks like Catherine may have died between 1850 and 1860 as she is not on the 1860 Census. James was born around 1853 so between then and 1860 to narrow it down a bit.
I also checked on FultonHistory.com to see if there was an obit or marriage notice posted in the paper but there was nothing there either.
Have you tried Castlegarden.org for them on the passenger lists?