There are 3 Michael's Duffy's in Sligo in the Griffith Valuation of 1858. Hard to tell if any of them are your Michael Duffy. www.askaboutireland.ie
There were place names for Culleen in Clare and Culleens in Mayo, and Culleenamore & Culleenduff in Sligo in 1858, and more. In the 2004 Atlas there is a Culleen, Clare and Cullens in Sligo.
Would they be in Ireland for the 1901/1911 Census?www.census.nationalarchives.ie www.genealogy.nationalarchives.ie
1823-1837 Tithe Applotments
Clare has no birth records I'm aware of on line, however, Sligo is on line with www.rootsireland.ie
foundation, not for profit but charge a fee.
If Michael & Winifred married after 1864 you might find
their marriage on www.familysearch.org
and any children they may have had. If they were born before 1864 baptism records are Parish records.
P.S. Thomas Coleman, Parish of Kilglass, Townland Culleens
Union of Dromore, West. tenant of Thomas Jones
38p house and land, land is shared amongst neighbours, about 400 acres.
Bryan Duffy, Parish of Kilglass, Townland Culleens, Union of DromoreW tenant of Thomas Jones
7c house, outbuildings and land shared
James Duffy, same info as for Bryan
40g house, outbuildings and land shared
Because of the date of 1858 the above are probably the grandparents, rather than parents.