I looked at findmypast.ie for baptisms of Sarah and Ellen and found none that match. I didn't see any Church of Ireland records in the results, so maybe they don't have them.
I thought I had read this somewhere, here is the link:
C of I records to come online soon:
https://www.irishtimes.com/life-and-style/abroad/new-digital-church-of-ireland-records-will-make-searching-for-ancestors-easier-1.3639993------
There are no Arthur Cunninghams on the 1901 Census of County Down who are old enough to be the father of Sarah and Ellen.
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In Griffith's Valuation of County Down, (1863-64), for Arthur Cunningham. (This assumes that Sarah's father Arthur was still alive in 1863, 1864.)
There are 8 men listed. I would concentrate on the first two, since they are not renting land.
Rathmullan Parish, Rossglass Townland, parcel 10c, house only,
Kilbroney Parish, Newtown Townland, parcel 15 Aa house and office
Kilkeel Parish, Aughrim Townland, parcel 7, house, offices, and land
Kilkeel Parish, Aughrim, 27, mountain, joint occupancy with many others
Kilkeel Parish, Dunnaman Townland, house, offices, and land
Kilkeel Parish, Leitrim Townland, parcel 8A, 8B, house, office, and land
Kilkeel Parish, Ballykeel Townland, parcels 43A, 43B, 43C, house, offices, and land
Kilkeel Parish, Moneydorraghmore, parcel 71, house and land
found at
http://www.askaboutireland.ie/griffith-valuation/----------
Arthur Cunningham deaths, in County Down, 1865 - 1922, at
https://www.irishgenealogy.ie/I eliminated all for which there were images, based on age at death or occupation. That left these three:
Name ARTHUR CUNNINGHAM
Year of Death 1875
Group Registration ID N/R
SR District/Reg Area Newry
Deceased Age at Death 74
Returns Year 1875
Returns Quarter 4
Returns Volume No 16
Returns Page No 586
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Name ARTHUR CUNNINGHAM
Year of Death 1869
Group Registration ID N/R
SR District/Reg Area Kilkeel
Deceased Age at Death 74
Returns Year 1869
Returns Quarter 2
Returns Volume No 6
Returns Page No 466
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Name ARTHUR CUNNINGHAM
Year of Death 1870
Group Registration ID N/R
SR District/Reg Area Kilkeel
Deceased Age at Death 70
Returns Year 1870
Returns Quarter 4
Returns Volume No 16
Returns Page No 397
The images of these are available, information on getting them is at:
https://www.irishgenealogy.ie/en/civil-records/help/i-want-to-get-a-copy-of-a-certificate-what-do-i-doHowever, I think more civil record images are coming online soon also, but I don't know what they include.
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I don't know where else to look in the Irish records. Maybe you can find a clue in the English records, an obituary or news clipping, etc., but probably not likely for a poor woman in that era. If you can tie any of the Cunninghams on the Isle of Man back to Rathmullan Parish, or Newtown Townland in Kilbroney, that might lead somewhere.
I think of Cunninghams and County Down as my "home turf" genealogically speaking, although I live in the US, so that caught my eye when I saw your question. I enjoyed working on it and I'm a bit disappointed that we didn't get anywhere -yet.
