In case this message initially reads like it's been posted under the wrong surname, in an incorrect forum, keep reading and all will become clear....
My Great Great Grandfather was Matthew McNiff, from the Townland of Lisnanaw, in County Leitrim, Ireland; my Great Grandfather was his second son, James McNiff, and my Grandfather his son John. In 1897 the family emigrated from Ireland to Edinburgh, Scotland, and at the end of 1897 had another son, Michael, who was christened McNiff.
At some point between 1897 and the 1901 Scottish Census the family surname was changed from McNiff to Duffy, in fact by the birth of the next child in Scotland, Francis Duffy, in 1900. We've no idea why the name was changed (and as far as I'm aware it wasn't done formally), that's lost in the mists of time, but this isn't an isolated case of the name change, there are other McNiff from Leitrim who also changed to Duffys when they came to Scotland.
So this is really to let anyone who runs into a brick wall tracing Duffys back to Ireland (I think specifically Leitrim) in the 19th or 20th century, that you're maybe not looking under the right surname, and might have more luck with McNiff or one of it's variations (MacNiffe, MacAniff....). Hope this is of help to somebody!