Hi Helina.
I don't envy you your task. As aghadowey says, without at least something to go on, it will be an uphill struggle.
I had a look on Emerald Ancestors and only came up with 4 results, 3 marriages and 1 census return.
1901 Census.
Julia Coole, age 29. Not married. Church of England. Townland of Crom. Parish of Galloon. County Fermanagh.
3 marriages.
Peter Foster married Betty Coole, on the 23 February 1868, in Feeny Roman Catholic Church, Parish of Banagher. Civil District Newtown Limavady. Co Londonderry.
David Moody married Emily Coole, on the 2 January 1879, in Tullylisk Church of Ireland, Parish of Tullylisk, Civil district Banbridge, Co Down.
James Richard Coole married Susan Glass, on the 25 February 1896, in Aghadrumsee Church of Ireland, Parish of Clones, Civil district of Clones, Co Fermanagh.
I think Lord Brookeborough's family home is called Castle Coole or Coolebrook, which I think is in Fermanagh. Someone else may be able to correct or add to this if I have got it right. It may or may not help.
Regards,
Dixie