Thanks to lots of new online resources I have found more details on the Ramsey family of the original request, so here's an update:
William Ramsey (c1836), son of Francis & Rose Ann, m.(28 June 1866 Co.Derry) Mary Jane O’Donnell. Known children:
1. Mary Jane Ramsey (29 Jan.1867, 5 Harvey St.-6 Feb.1867 Harvey St.).
2. Thomas Ramsey (29 Jan.1867, 5 Harvey St., Derry).
3. Henry Ramsey (14 Apr.1868 Harvey St.-20 May 1868, Harvey St.).
4. Rosanne Ramsey (22 June 1869 Fort Hill St., Enniskillen). died 1871 Enniskillen dist
5. Mary Jane Ramsey (1 Mar.1871 Enniskillen). died 26 Aug.1895 Derry (thanks DoireM)
6. William Ramsey (16 Aug.-16 Aug.1873, Harvey St.).
7. Anne Ramsey (16 Aug.1873 Londonderry-d.y.).
8. William Ramsey (23 July 1874 Derry). died 1936, married Mary McGowan
9. John James Ramsey (21 June 1877, 7 Harvey St., Derry).
10. Anna Eliza Ramsey (21 Oct.1879 Derry).
11. Francis Ramsey (c8 July 1882 Wapping La.-18 July 1882 Wapping La.).
12. Francis Ramsey (30 Oct.1884 Derry-20 Oct.1916) m. Annabella Johnston