Dear Amanda
ps I did a place search of LDS family search:
Topic  England, Cumberland, Cockermouth - Church records
 
Titles  Births and baptisms  Independent Church (Cockermouth) 
Bishop's transcripts for All Saints Church, Cockermouth, 1689-1862  Church of England. All Saints Church (Cockermouth, Cumberland) 
Church records, 1841-1910  Wesleyan Methodist Chapel. Cockermouth Circuit (Cumberland) 
Cockermouth miscellanea  Cumbria Family History Society 
Parish registers, 1632-1881  Church of England. All Saints Church (Cockermouth, Cumberland) 
Parish registers, 1865-1883  Church of England. Christ Church (Cockermouth, Cumberland) 
You may be able to search these records at the LDS centre closer to you, I see they have no RC records.
They also have all the censuses 1841-1891 for Cockermouth
Pat