Katherine,
The name Minnie is found fairly widely in Scotland & Ireland. People are sometimes given it as a birth name – I can see about 3000 of them in Ireland in the years 1864 to 1916 - but it’s frequently a diminutive. I searched for a Minnie birth around the time indicated by the English census. I didn’t find one that fitted, so I looked for likely alternatives and quickly found Mary. Since her date of birth and father’s name and occupation tie in with the information you already have, then it seems pretty certain it’s the right family. Plasterer isn’t that common an occupation, so I think it’s pretty unlikely that there would be 2 families of the same name and occupation with the right number of children of the right ages, at the same time. I’d be about 99% certain this is the right family.
You ask how I found the other birth, ie Anne Louise. I used a searching trick. Though Northern Ireland births are available free on the Irish genealogy site, those in earlier years on that site don’t show the mother’s name in the indexes. However the GRONI website which contains the same records does show mothers names. So what I did was enter the parent’s surnames Wiley/Wylie and Russell, and leave the child’s forename blank. This search threw up just 3 children in the period 1864 to 1880. One was Mary we already had and another was a female birth to the same parents and fathers occupation, at about the time you know Anne Louise was born. So it has to be the same family. I didn’t find any other children after 1870 and that’s quite important. If this were a different family who stayed in Ireland, you might expect them to have had a few more children. But they don’t. So that’s indicative that they had left Ireland. Just around the very time your family turn up in Newcastle on Tyne. QED.
As far as Catherine is concerned, I suspect the family were probably Church of Ireland so I’d be inclined to search the COI baptism records for Magherafelt (where they married) and Clogher (where Anne Louise was born in 1865) for the years 1862 & 1863, on the basis that they were probably living in one of those 2 parishes at that time. Neither of those parishes records are on-line yet. However there are copies in PRONI (the public record office) in Belfast. A personal visit is required to view them.
Tradition was to marry in the bride’s church, which was Magherafelt Church of Ireland. So she seems to have been COI. It’s possible that she came from that parish. Searching those records for her baptism might find siblings and her parents. However I note that she was a servant, and so she probably wasn’t living at home with her family, and so quite where she came from may be a mystery. Her father was John Russell, farmer. I searched Griffiths Valuation for 1858 and did not find any farmer of that name in Co Derry, nor any farmer of that surname in Magherafelt parish, so can’t suggest where she may have come from. (Her father may have been dead or she may have come from another county).
Mary was living at Gravesend when she married. That was a big house, named after a Rev Graves who presumably built it, near Castledawson. I’d expect she was a servant at that house. It’s in Shanemullagh townland. Today it’s the clubhouse for Moyola Golf Club.
You say you can’t find the births on the irishgenealogy site. Are you searching under civil records? That might be the mistake.
A couple of things to add to previous information. Firstly, at the time of the birth in Fivemiletown, the father’s address was given as “believed to be at Belfast”. So he had presumably gone to Belfast to work. I’d wonder what the family were doing in Fivemiletown. Perhaps James had been working there and gone to Belfast leaving his family behind. Or perhaps that’s where one of their parents lived, and Mary and her children were staying there.
Secondly, I forgot to tell you I found another child to James & Mary. James Wylie was born at 57 Nelson St, Belfast on 29.9.1867. Same parents and occupation. There’s a James Wiley death in Belfast on 7.5.1868 aged 0 which may well be him. That death certificate is not on-line free yet, and so if you want to check it out, you can view the original on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.