Judy,
Statutory birth, death and marriage registration (in some jurisdictions called Vital Records) only started in Ireland in 1864, save for non RC marriages which were recorded from 1845 onwards. So you probably won’t find statutory birth, certificates in Ireland for these 2 families. For earlier years you usually need to rely on church records, where they exist. Ideally you need to know the precise denomination and have some idea of where the person was born in order to search the correct records. Not all churches have records for that period and not all are on-line.
I note the marriage was in a Register Office so I can’t draw any conclusions about their denominations from that. Isabella was evidently from Lissan. There are 4 townlands in Ireland named Lissan as well as a parish, so the question is which Lissan is the right one? The parish is partly in Co. Tyrone & partly in Co Londonderry. The McIver/McIvors in Tyrone in the 1901 census were an even mix of Catholic and Presbyterian. There were well over 600 Andersons, a mix of all denominations.
I looked in Griffiths Valuation for a Thomas Anderson from Lissan parish (Tyrone) but did not find one. I did find one in the Co. Londonderry part. In 1859 he lived in Dunnabraggy, but he was a labourer not a farmer, so far as I can see.
The Church of Ireland in Lissan has records as follows:
Lissan (Armagh diocese)
Baptisms, 1753-95 and 1803-95; marriages, 1744-94 and 1805-46; burials, 1753-95 and 1805-43; vestry minutes, 1734-1816; publication of banns, 1805-1904; confirmations, 1824 and 1828.
There’s a Presbyterian church there at Claggan with records as follows:
P. Claggan
Baptisms, 1846-1916; marriages, 1848-1931.
The local RC church has:
Lissan (Armagh diocese)
Baptisms, 1839-81; marriages, 1839-80.
Fragments of baptisms, 1822-39, and marriages, 1822-30.
The RC parish records are on-line free on the National Library site:
https://www.nli.ie/en/family-history-introduction.aspx
The Church of Ireland & Presbyterian records are in PRONI (the public record office) in Belfast. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
I did not find a Daniel McIvor in the parish of Lissan but I did find one in the townland of Lissan in the parish of Drumragh. He had plot 4 there in 1860 which was a 34 acre farm. So I wonder if Lissan means the townland rather than the parish? No Andersons in the Drumragh Lissan though.
The Valuation revision records (on the PRONI website) show the Lissan property changing from Daniel to John McIvor in 1871 before changing again to the Miles family in 1880. There’s a possible death for Daniel McIver on 14.6.1870 aged 66 registered in Omagh (which is where a death in Drumragh would be registered). I don’t know for certain that it’s your family but it is the only death in Tyrone that I can find that might fit. You can view the original certificate 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. There are a number of trees on Ancestry which have this family and many give the above death as “your” Daniel. His wife’s name was given as Martha in some trees (no dates).
You could search the records for the churches in Drumragh parish. (There are about 10). The details are on the PRONI website:
https://www.nidirect.gov.uk/publications/proni-guide-church-records
The RC records are on the nli link given above. Accessing the others will involve a trip to PRONI.
I will have difficulty finding Thomas Anderson on the available information because it is such a common name. There are dozens of them. I don’t see anything to link any of them to a Lissan though.
