According to Letitia Atkinson’s death certificate, her husband Stewart was still alive in 1889:
I have looked for a death for him post 1889 but without success. Possibly his death wasn’t registered. That did happen. Looking at the Valuation revision books I see that the farm passed from Stewart to William in 1892. So that points to Stewart’s death around that year.
Statutory marriage registration started in Ireland in 1845. Prior to that you have to rely on church records. Not every church has pre 1845 records, and where they do, they are not always on-line. Lismoyle is in Tamlaght O’Crilly parish. The family were Presbyterian (judging by the 1901 census). Nearest Presbyterian churches seem to be Boveedy (records start 1841) and Churchtown (records start 1839). Another possibility is Garvagh 2nd Presbyterian church. I see that’s where Thomasina married. Tradition was to marry in the bride’s church so possibly that is the family church. If so, their baptism & marriage records start in 1830 and interestingly they have burials for the years 1853 – 1896. Most Presbyterian churches didn’t keep burial records so that’s a bonus. If Stewart died around 1892 and attended that church you might find his burial record there.
You’ll perhaps know which church the family attended, but if any of these 3 is where Stewart & Letitia married in 1835 and were themselves baptised in the early 1800s, then there are only marriage records for Garvagh 2nd. No baptisms for the early 1800s (though you may find their childrens baptisms post 1840). It doesn’t look to me as though you will find baptism records for Stewart or Letitia. They probably don’t exist. Copies of all the surviving records are in PRONI in Belfast. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
I noticed this probate abstract for William Atkinson on the PRONI wills site:
Atkinson, William of Lismoyle Swatragh county Londonderry farmer died 11 February 1924 Administration (d.b.n.) Londonderry 8 November to Mary Sarah Bolton widow. Unadministered effects Nil. Former Grant Administration London D.R. 6 February 1925.
It looks as though when William died in 1924, he died intestate and his estate was not fully administered, something apparently not picked up till 1961. (Probate granted 8.11.1961 Londonderry). It also looks as though he had assets in England as there was a probate grant there in 1925. (Possibly an insurance policy or investments).
Coleraine Chronicle of 23.9.1899 reports that William Atkinson of Lismoyle had a nasty accident whilst threshing hay and one of his fingers had to be removed.
Regarding the Atkinson family in the 1841 Scottish census, in that census only, adults ages were rounded down to the nearest 5 years. So 25 means anything from 25 to 29 and 20 means 20 to 24.
Most Irish research comes to a stop around 1800 due to the lack of records. It’s a common problem.