Shelley,
The tithe applotment records for 1829 list 2 McAteer farms in Mulnahunch, one headed by John and the other by James:
http://www.cotyroneireland.com/tithe/killeeshil.html
Griffiths Valuation for 1860 lists a William McAteer farming on plot 7A in Mulnahunch which was a 20 acre farm. (Today that’s up a dead end lane off the Killeeshill Rd). Presumably that’s some relation of Margaret’s.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch
The revaluation records show the farm remaining in William’s name till 1884 when it changes to William James McAteer (suggesting William may have died). (There’s a couple of possible deaths 12.2.1883 aged 82 and 2.8.1885 aged 70, both registered in Dungannon).
Family in 1901:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Clananeese/Mull…
And in 1911:
http://www.census.nationalarchives.ie/pages/1911/Tyrone/Clonaneese/Muln…
In 1924 it changes to Thomas J. McAteer, again suggesting the farm has changed hands on William James’s death. Those records stop in 1929 (though there are later records in PRONI in Belfast which show subsequent ownership. They are not on-line though.
https://www.nidirect.gov.uk/proni
Probate abstracts from the PRONI website:
McAteer Margaret Jane of Mulnahunch Cabra Donaghmore county Tyrone died 7 April 1930 Administration Belfast 5 June to Thomas John McAteer farmer the husband. Effects £1342 7s. 6d.
McAteer Joseph of Mulnahunch Cabragh Dungannon county Tyrone retired farmer died 20 September 1958 at South Tyrone Hospital Dungannon county Tyrone Administration Belfast 26 March to Elizabeth Isobel McAteer spinster. Effects £2864 8s. 10d.
The above probate files should be held in PRONI in paper format.
The family were evidently Presbyterian. The 2 nearest Presbyterian churches appear to be Clonaleese Upper which has records from the 1860s and Clonaleese Lower which has records from 1811 (baptisms) and 1845 (marriages). Copies of both churches records are in PRONI. They are not on-line anywhere so far as I am aware.