A few bits I found yesterday when searching which might be useful-
Sarah Nicholson (c1829/c1825 Ire.-1911 Beech Hill)
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1911/05388/4504071.pdfIn at least one census she is listed as sister of Edward Nicholson, If this is the case perhaps half-sister? Certainly much closer in age to William Nicholson (architect) and his siblings.
Edward Nicholson & wife Margaret-
Derry Journal, 24 Dec.1883: Death of Mr. Edward Nicholson, J.P., Derry. —This gentleman died at his residence, Beech Hill on Thursday morning. The deceased was a native of that of that district, and had in early life gone Manchester, where ...
Derry Journal, 17 Feb.1892: Nicholson —February 15, at Beech Hill, Margaret, relict of the late Edward Nicholson. Will be buried Ardmore Catholic Burial-ground on Friday, 19th inst., at eleven o’clock.
Can't remember if this was posted earlier.
1851 Census (Edward Nicholson)-
https://www.familysearch.org/ark:/61903/1:1:SGYC-7YT Edward's son Richard Alfred Nicholson died 2 Dec.1889. His daughter-
Cork Constitution, 13 Feb.1894: ... Rev. Father Croskell, Thomas Francis Malian, Ardmore, county Derry, to Edith Mary, daughter of the late Richard Nicholson, of High Bank, bandiway[?], Altrincham. Cheshire, and granddaughter the late Edward Nicholson, JP, of Beech Hill, county Derry.
Edward's daughter Mary Birch Nicholson-
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1904/05611/4577896.pdfWeekly Irish Times, 19 Nov.1904: NICHOLSON—November 12, Beech Hill, Londonderry, Mary Birch, only daughter the late Edward Nicholson. R.I.P.
http://www.willcalendars.nationalarchives.ie/search/cwa/details.jsp?id=1639426054