Robert Meldrum farmed in Doogary, parish of Kilskeery, Co. Tyrone.
There’s this family farming there in 1901:
https://www.census.nationalarchives.ie/pages/1901/Tyrone/Drumharvey/Doogary/1740402/
Same family in 1911:
https://www.census.nationalarchives.ie/pages/1911/Tyrone/Drumharvey/Doogary/869201/
Probate abstracts from the PRONI wills site:
Meldrum Anne Jane of Doogary (Irvinestown P.O.) county Tyrone widow died 7 April 1916 Administration (d.b.n.) (limited) Londonderry 9 November to William James Hamilton solicitor's assistant. Unadministered effects £35. Limited Grant. Former Grant Administration Dublin 8 December 1916.
Meldrum James of Doogary (Irvinestown P.O.) county Tyrone farmer died 22 November 1949 at the General Hospital Omagh in said county Probate Londonderry 16 March to Edward Ernest McClintock farmer. Effects £277 5s.
Anne Jane died intestate (no will). James did leave a will and it should be in PRONI (in paper format, so not on-line).
Jane Meldrum’s birth in December 1883 from which we know her father was John and mother Ann Jane Brunt:
https://www.irishgenealogy.ie/files/civil/birth_returns/births_1884/02702/1995009.pdf
So that looks to be the Johnnie mentioned in Margaret’s letter. Here’s his marriage in 1871, father Robert:
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1871/11361/8170754.pdf
Ann Jane’s brother Ralph happens to be married on the same page, 2 months before her marriage.
John Meldrum died in 1890, aged 42.
https://www.irishgenealogy.ie/files/civil/deaths_returns/deaths_1891/06081/4734444.pdf
Here’s a Margaret Meldrum of Doogary who died in 1872 aged 22. Possibly Robert & Margaret’s daughter?
https://www.irishgenealogy.ie/files/civil/deaths_returns/deaths_1872/020747/7278669.pdf
She was born before the start of birth registration (1864) so you would need to check local church records for her baptism. (They can be viewed in PRONI in Belfast).
Here’s what looks to be Robert Meldrum’s brother Christopher’s marriage in 1861:
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1861/09610/5485349.pdf
Again on the same page, you will find his widowed sister Jane re-marrying to Robert Robinson. That part of the family were farming in the townland of Relagh Guinness. Here’s Jane’s first marriage:
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1848/09353/5386839.pdf
I looked for Margaret Meldrum’s death but did not find one with any certainty. There is one in the area on 27.7.1871 aged 73 which is pay to view. She looks too old to me (Mgt was born c 1818) but ages can sometimes be out by a few years on death certificates. The Valuation Revision records on the PRONI website show that Robert Meldrum had plot 2 in Doogary which was a 10 acre farm. His name is deleted in 1866 with “dead” noted beside it, and he was replaced by Margaret. She in turn is deleted in 1884 and replaced by John and then after his death by his widow Ann Jane. The years note when Griffiths Valuation clerks learned of the change, rather than when they necessarily happened, and so can be out by a year or two. So it looks as though Robert died before 1864 (when death registration started) and that Margaret died around 1884, though I don’t see a death that fits.
As to which graveyard the Meldrums might be buried in, I would try Kilskeery Church of Ireland, failing which Kilskeery Old graveyard.
Fermanagh Herald of 9th Jan 1904 reports that James Meldrum and his mother Ann were both summoned by Thomas Hetherington of Doogary for assault & trespass. They lodged a counter case against Hetherington alleging he assaulted them. Hetherington won the case and was awarded 1 shilling damages for the trespass.
You ask if I have any idea who James Wray was married to, and where he is buried. No idea at all to either question.
If you have checked the Drogheda Church of Ireland records on the link Pat provided, you will note that there is no sign of a burial for James, nor baptisms for all the children you have listed. Apart from the gravestone inscription, do you have any other record that links the Wray/Rea family to Drogheda? (Which is in Co. Louth by the way, not Co. Meath. Could the gravestone be wrong about Drogheda too?) I wonder if perhaps they really come from Tyrone. I’d get a researcher to look at Kilskeery Church of Ireland records in PRONI to see if the children were baptised there. And you may well get James’ burial there too.You might also find his marriage.
For professional researchers in Ulster, try the Society of Genealogists:
http://sgni.net/
If you are interested in the origins of the Meldrum name, MacLysaght’s “The Surnames of Ireland” says it is “Derived from a Scottish place name, this name had been in Ulster and North Connacht since the Plantation of Ulster early in the 17th century.” So the Meldrums probably originated in Scotland, perhaps near Old Meldrum in Aberdeenshire, and moved to Ireland in the early 1600s. (Some 200,000 Scots settled in Ireland in the 1600s so that’s a pretty common family background, especially in Ulster).
