There was no Logan household in Craigbrack in the 1831 census. The only John Logan in the parish was this one:
This looks to be Elizabeth’s father in Bolie in 1831:
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Tirkeeran/Faughanvale/Boleas/1/ Family was Presbyterian at that date (though Elizabeth married in the Church of Ireland).
John Logan is listed in Griffiths Valuation for Craigbrack in 1858. The property he had was plot 3b which was a labourer’s cottage. Thomas is deleted between 1860 and 1865. Given that there is no death certificate, I’d agree he probably died before 1864. Likewise for wife Mary as I cannot see a death certificate for her.
I searched for births to parents Logan & McIlhatton 1864 to 1873 but without success. For records prior to 1864 you would need to search church records and to do that you would need to know which church they attended.
I don’t see any deaths for Elizabeth Logan in the Londonderry/Limavady area. Could she have died before 1864 too?
Faughanvale Church of Ireland birth, marriage & burial records start in 1802. Faughanvale Presbyterian church has baptisms from 1819 but no marriages before 1845. Copies of both sets of records are held in PRONI in Belfast.
Both Thomas & Elizabeth are aged 20 when they married in 1858 so born c 1838.
If the Logan family were Church of Ireland you may find burial records for John & his wife Mary as well as perhaps Elizabeth Logan. Presbyterians generally didn’t keep burial records and there are none shown for Faughanvale.
Finding much more information on John Logan may be tricky.