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The RC records for the parish go back to 1813 for baptisms and marriages. http://registers.nli.ie/parishes/0109 I would search on www.irsh genealogy.ie under the Church records TAB. That site has the records for Enniskeane/Desertserges parish and all other parishes in the Diocese of Cork and Ross. Hopefully, you will find leads for the baptismal records for James and Mary which will include their parents names.
I don't see a John Mahoney/Bridget Buckley marriage record around 1860.
Finding death records will be difficult because the names are very common. I believe they would have died in the Clonakilty registration district. Right now only images of death records are available from 1891-1940 at www.irishgenealogy.ie Civil records TAB. We are expecting that images for 1864-1890 will be available possibly later this year and then you can search for the records for James and Mary.