All bmd records before 1864 are Parish records.
Tithe Applotments: 1824 there are Owen & Thady Tigue in Sligo occupying land www.genealogy.nationalarchives.ie
Griffith Valuation 1856 is the next record used as a census substitute. There are the following listed for Sligo:
James, Denis, John x 2, Terence, Charles, Thomaswww.askaboutireland.ie
No Francis Tigue in Sligo, however there is one in Mayo.
Francis Tigue, Parish of Aghamore, Townland Mannin
Poor Law Union Swineford, tenant of Margaret Mary Beaty
#8b house and 1/2 share of land 15 acres 2 roods 23 perches
Sligo belongs to an Irish History Foundation a pay website although none profit. Depending on the parish you should be able to find Margaret Tigue's birth record. A birth record gives parish/place, date, mother's name and maiden name.
Belmullet, Mayo: birth records 1841-1900, marriages 1836-1900 so you should be able to find her birth record
Margaret's children should relect her parents names!
There are 3 Tigue's listed in the Mayo Telephone Book. Quite a few Gaughan's including some in Belmullet, Mayo.