My 2nd great grandmother was Jane Duffy, who married Bartholomew Loughney in Kincon, Kilfian Parish, County Mayo in 1836. I have been trying to trace further back, but records are quite poor beyond that. I believe she had a brother Michael Duffy, based on Parish records, but no proof as of yet. There were more Duffys in Lacken Parish, but I don't know if they were related.
This has made me research a bit more on the name Duffy:http://www.libraryireland.com/names/od/o-dubhthaigh.php
From Irish Names and Surnames 1923
Ó DUBHTHAIGH—I—O Duffie, O Duhie, O Duhig, O Dowhie, O Dowey, O'Duffy, Duffy, Duhy, Duhig, Dowey, Douey, Dooey, Doey, &c, and sometimes, by translation, Black; 'descendant of Dubhthach' (black). This surname is found in all parts of Ireland, and, doubtless, there are several distinct families so called. The O'Duffys of Connacht are remarkable for the number of eminent prelates they formerly gave to the church in that province. The O'Duffys were also a family of note in Monaghan. In Munster, the name is generally anglicised Duhig, owing to the pronunciation of the final g. The family is, according to Keating, of Dalcassian origin. In Ulster, where the name is very common, especially in Monaghan and Donegal, it is sometimes anglicised Dowey and Dooey. See Ó Dúithche.