Many thanks for your quick response. I have trawled through the many census returns and BMD certificates both in the UK and US in which my family appear and so far no place name is mentioned. However another Duffy family, who were neighbours in Huddersfield, were from Swinford, Co Mayo, though I can't prove a relationship, except the Swinford Duffys were one of the first Duffy families to arrive in Huddersfield (there were about 6 or 7 in 1851) and my family appear to be the last. This area of Mayo is reasonably close to the Sligo border so that would fit my Grandmother's story that they came from the Sligo/Mayo border. There is also a strange entry on a US Federal census which states Ann Duffy, the daughter b.1843, as being from Maine. This was on a census some 30 years after her death in New Jersey, filled out by a son-in-law who never knew her, so he may have mistaken Maine for Mayo.
James Duffy was born 1801 and Ann Duffy 1804. They must have married some time between 1822 and 1828. Their first child Patrick was born in 1829. They were Roman Catholic. I know a lot about what happened to them once they arrived in England (about 1848) but nothing of their life in Ireland.
In your view, is it worth starting with the Parish records for Swinford for this period and working outwards and towards and into Sligo or would this be too greater task? If not, is it possible and how do I go about it? Many thanks.