Dear Mary
Welcome to Ireland Reaching Out and thanks for your query
As you can see from the link below Kilcatherine is a Civil Parish in Co. Cork:
http://www.irishtimes.com/ancestor/fuses/townlands/index.cfm?fuseaction=TownlandsInCivil&civilparishid=235&civilparish=Kilcatherine&citycounty=Cork
The records for the corresponding Roman Catholic Parish of Eyeries begin in 1824, though baptism records did not begin until 1843.
On that basis you could search www.familysearch.org or www.irishgenealogy.ie for a records of any Driscoll ancestors. On the family search site you should also be able to locate a civil record of Michael and Lizzie?s birth (as well as any other children), as civil registration began in Ireland in 1864 (generally speaking). A civil record should provide you with the names of the previous generation, so you should also conduct a search for the marriage record of Jeremiah and Mary.
As an aside, you may also be able to find a record of Jeremiah on the Tithe Applotment Books 1823-1837. Although only the heads of household are mentioned it can be useful:
http://titheapplotmentbooks.nationalarchives.ie/search/tab/index.jsp
The Griffith?s Valuation 1847-1864, a land survey, may also list Jeremiah and it can be searched for free, here:
http://www.askaboutireland.ie/griffith-valuation/
Once you have the townland details from the above records, you could as a matter of general interest, search the 1901 and 1911 Census to see how many Driscoll families lived in the area during that time:
http://www.census.nationalarchives.ie/search/
Best of luck with your search and your travel plans
Clare Doyle
Genealogy Support