Sorry, I just realized I said something inaccurate in my previous post. The name of the place of Mary Finn's birth I found on her daughter's death cert in Chicago, which obviously is even further removed and even more likely inaccurate. I found a brief article on ancestry.com on Mary Finn, in the database "Chicago Irish Families, 1875-1925" that said this:
"Dwyer, Mary, nee Finn, was buried Sept. 6, in Calvary. She died at her residence, 370 Orchard st. August 27, aged 77 yrs. She was born in Tipperary, Ireland and when a girl in her teens came to America, locating in Montreal, Canada. Then she was married to Andrew Dwyer, 52 years ago. After a short stay in Canada, the family moved to New York state from which place they drifted west eventually to Chicago, and residing here nearly thirty years. Three children survive her, John K., and James P. Dwyer and Mrs. James P. O'Connor. -Sept. 15, 1894"
So according to this source, at least the county of Tipperary is correct. I will appreciate any help with this question of her specific birthplace.