I don?t see any Cuthbert households in Culmore in the 1831 census. However there was a Robert Cuthbert nearby in Clooney, in Clondermot parish. Possibly the same person and he moved sometime between 1831 and Griffiths Valuation?
Presbyterians in Ireland don?t use the parish system, so which church they attended would have been a matter of personal preference. There were several in that area. However tradition was to marry in the bride?s church, so I?d be inclined to note which churches Fanny and her sisters married in, and then start your search with that churches records for baptisms etc.
You can see what Presbyterian records exist in Derry on the PRONI website. The records themselves are not all on-line and you may need to make a personal visit to PRONI to search them all. Not all have records that go back to 1827.
Robert appears to have died intestate in 1877. Est year of birth 1800.
From the PRONI wills site: Full Abstract :
Letters of Administration of the personal estate of Robert Cuthbert late of Culmore County Londonderry Farmer deceased who died 25 December 1877 at same place were granted at Londonderry to David Cuthbert of Coolkeeragh in said County Farmer the Son. (By Decree of County Court Judge.) Effects ?299