Dawn,
Few graveyards in the 1800s kept burial records. The Church of Ireland was the only denomination that routinely kept them though even then I have found many gaps, and they tended only to record their own denomination, not burials by other denominations.
There are transcriptions of the legible gravestones for some graveyards in Co Down. The Ulster Historical Foundation has some Co Down graveyards on its site:
http://www.ancestryireland.com
I had a quick look. There are 12 Rainey gravestones listed in Co Down but none for the parish of Newry. So possibly the graveyards in that parish haven’t been transcribed.
I note that Savalmore graveyard in Savalmore townland is immediately adjacent to Castle Enigan. It’s on the modern Coalpit Rd. Ouley graveyard is also close by near the modern Shinn Rd. They are probably the 2 most likely burial places for your Raineys.
I should certainly contact the Smith family to see if they have any additional information. There are actually 13 trees on Ancestry with the family. All seems to have much the same information, suggesting they come from a common source.
Looking at the 1875 marriage certificate, I see that Isaac was living in Castle Enigan then. The certificate also tells us that his father was dead by that date. I notice that the couple married in a Register office, not a church. There can be many reasons for doing that. One was a mixed denomination marriage (usually Protestant – Catholic), another might simply be that neither party was religious or sometimes it could be because they were Brethren. Brethren normally marry in a Register Office (because they don’t have anyone qualified to conduct a marriage service).
I looked at the Valuation Revision records (On the PRONI website) for 1875 to see if Isaac Rainey is listed in Castle Enigan. He’s not. The only Rainey there was a David Rowney who had a labourer’s cottage plot 3B© (on the modern Castle Enigan Rd). That cottage looks to be long gone today and there’s a modern house there now. David might be a relation. His name remained as tenant till the mid 1880s. I don’t see a death for him.
I noticed a death for a Sarah Rainey aged 15 in Castle Enigan in 1892. Mother was Eliza Rainey.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1875/11210/8108896.pdf
Here’s her birth in Castle Enigan in 1878. She was illegitimate:
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_retur…
As I mentioned previously, we know Thomas Rainey was dead by 1875. I don’t see a death certificate for him 1864 to 1875, so my guess is that he died 1855 – 1863.
No Rainey/Rowney households in Castle Enigan by the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/Down/Ouley/Castle_Enigan/
You ask how you would locate living descendants today. I have to say that it can be quite difficult. It’s a common name in the area, and the likelihood of anyone in Shinn or Castle Enigan today knowing directly of a family that moved away at least 130 years ago does not seem high. However you know that your family attended Donaghmore Presbyterian church. You could contact the current Minister and ask him if there are any Raineys in the congregation today. Or possibly the church has a facebook page and you could post a message there. The current Minister appears to be Rev Raymond McKibbin and his contact details are on this link:
https://www.glascar-donaghmore.com/aboutus
PRONI has the following records for Donaghmore church:
Donaghmore Baptisms, 1804-37 and 1845-1968; marriages, 1845-1936. If you haven’t already done so, it would be worth going through them looking for other children etc.
You mention that Isaac born 1854 was born in Loughorne. That’s immediately beside Shinn & Castle Enigan. Griffiths has a Rosanna Rainey and an Alexander Rainey in Loughorne in 1864, so perhaps relations. Alexander had plot 25c which was a flax mill, yard & mill race. Rosanna lived nearby on plot 23 which was a labourer’s cottage and garden. She was probably a widow. Rose Anne Rainey probably died in 1871 aged 80. That certificate is not available to view free yet. You have to pay to view it on the GRONI site (cost £2.50).
Alexander Rainey of Loughorne was born c 1818, son of Joseph Rainey, and he married Rebecca Clegg in 1848:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1848/09355/5387788.pdf
Though the 1851 Irish census was destroyed in the 1922 fire in Dublin, an 1851 census extract survives for this family (due to it being copied in 1921 as proof of age for a pension application) which tells us that in that year Alexander & Rebecca’s family consisted of Mary aged 2, Anne & Elizabeth (no ages) and Rebecca’s father David Clegg. There also appears to have been a son Joseph Rainey who was reportedly born 26th June 1850, and who was still alive in 1921 (when he applied for an old age pension). He was living in Manchester at that time. The family are on a tree on Ancestry (Fletcher family) and that shows Rebecca Rainey dying in Ashton under Lyne (just outside Manchester) in 1903. So the family had evidently moved to England for work.
http://censussearchforms.nationalarchives.ie/search/cs/home.jsp
Labourers in Ireland often took cottages on short tenancies or “at will” terms ie they could leave with no notice. This enabled them to move to follow available work. So it’s common to find them moving from one townland to another. They can be tricky to trace.
Given their location in Co Down and their denomination (Presbyterian) your family are probably descendants of Scots who settled in the area in the 1600s.