County Tyrone Ancestors

You haven’t said what denomination the families were.  Looking at the 1901 census of Tyrone, the Nethercote/Nethercoat households there were all Church of Ireland.  If Margaret was that denomination at birth, the baptism, marriage & burial records for Donaghenry start in 1733 (with some gaps), though my guide to Church records says the earlier entries are “unintelligible” presumably because they have faded.  The records don’t appear to be on-line anywhere but there is a copy in PRONI (the public record office) in Belfast. Personal visit required to view them.

I can see that the couple married in the RC church so possibly this is a mixed marriage and Margaret converted to Catholicism. If she did you will often find an adult baptism record for her in the RC parish records, typically a month before the marriage.

The RC records for Donaghenry start in 1822 (with some gaps). So getting back earlier than 1822 for an RC family will be difficult if not impossible. The RC records are on-line on the nli and other sites eg Ancestry.

Judging by the 1834 tithe applotment records neither the Kelly nor Nethercot families were farmers. So they’d likely have been agricultural labourers. They tended to move about a little to follow the available work. Can make then hard to trace.

http://www.irishgenealogyhub.com/tyrone/tithe-applotment-books/parish-of-donaghenry.php

I looked in Griffiths Valuation (1859) and there were no Kelly households listed in Mullantain nor Nethercote in Tullylig then. Death registration didn’t start in Ireland till 1864 so if Patrick and Margaret died before that then there will not be a record.

One tree on Ancestry (File of Big Jays) records an additional son William born 1846 and also that Patrick died in Dublin in 1886.  The first William is shown as dying in 1826, explaining why the name was reused in 1846. That was a common tradition. The tree also shows Margaret dying in 1908 (making her 105) in Dublin. Not impossible but surprising.  Going by information on that tree, this appears to be Patrick & Margaret’s son Patrick in the 1901 census:

http://www.census.nationalarchives.ie/pages/1901/Dublin/Trinity/Hamilton_Row__Part_/1310805

No sign of Margaret in the Co Dublin area in the 1901 census, so her death there in 1908 needs verified.

In the 1796 Flax Growers list, there is one entry for a name similar to Nethercote in Tyrone:

Neathercoat George Donaghenry Tyrone

This shows the family was in Tyrone in 1796.