Juice,
Faughanvale RC parish has no baptisms records earlier than the 1860s so if that’s where your ancestor was baptised then sadly no records survive.
The 1831 census for Co. Derry has survived. There are only 2 Campbell households in Faughanvale. Both lived in Donnybrewer. Robert & Hugh Campbell. They lived beside each other so were probably related. Both households were Presbyterian.
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Faughanvale/Donnybrewer/7/
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Faughanvale/Donnybrewer/8/
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. If you have already tested your DNA with Ancestry, My Heritage or 23&Me you can upload your DNA results to Family Tree DNA for free and then join the North of Ireland Family History Society DNA Project. Simple instructions on how to do this can be found here: https://www.nifhs.org/dna/uploading-your-dna/