WELCOME ! It seems you know it is SLIGO, so I am sure with a little time and effort doing internet searches you can find out as much as you want. Have you Googled the Surname Tosney?
To start, I would immediately interviewing Mom AND Nanna for genealogy information - NAMES, PLACES (County and Townlands and DATES if possible).
Where were they from?
Write it down,ask for spelling but if they do not know do your best.
TOWNLANDS is the most important information -- where they lived is the Key. Census, Griffiths Valuation of Tenements, Tithe List can be searched free *(llok for my post Free Searching and follow the links, when you come to search boxes choose COUNTY, or TOWNLAND then Surname and search. Back and forth repeating this is all that is needed, print anything you come up with.
Start with the 1901 and 1911 Irish Censushttp://www.census.nationalarchives.ie/search
Good Luck, others can answer as well if you get stumped post back here on the Sligo (or whatever) County pages!