Thank you very much Pennines and Myluck for that information.
I had a feeling the children may have been baptised in a Protestant church, as I wasn't able to find the baptisms of William and 'Annie' recorded in any of the Catholic churches around Derry city.
Isabella Duffy seems to have been a Roman Catholic, according to my research, so Patrick Brown was presumably of the Established Church. It is unusual that their marriage is not recorded, unless they were married prior to the registration of civil marriages in 1845.
I possibly have found a marriage for their son William.
William Brown married Ann Jane Smith in Derry city on August 4th 1890.
They are recorded in the 1901 census as living at Ferguson Street, Derry city. In the 1911 census they are recorded as residing at Orchard Row, Derry city. William's unmarried older sister, Elizabeth (Lizzie) Brown, is recorded as living with the couple on both censuses. Their religion was Church of Ireland.
However, I've had no luck finding marriages for any of the other children of Patrick and Isabella.
Thanks again!!!
Best wishes,
Brendan