Hi
You really need one of the childrens birth certificates to find Sarah's maiden name and then work backwards from there.
There is a possible marriage (from freebmd)
Marriage June qtr 1859
Bowerbank John Cockermouth 10b 685
Doron John Cockermouth 10b 685
Hayton Sarah Cockermouth 10b 685
Walker Elizabeth Cockermouth 10b 685
A tree on A***try has this couple as parents of Ann, Ellen, Robert, Francis, William, James and Sarah but this information should always be checked.
The marriage cert should give Johns fathers name unless he was illegitimate.
Rosie