Dear Paddy
Welcome to Ireland Reaching Out and thanks for your query.
As you can see from the link below, Kanturk is in the Civil Parish of Clonfert http://www.irishtimes.com/ancestor/fuses/civilparish/index.cfm?fuseaction=GetMap&CityCounty=Cork&UserID= The Roman Catholic Parishes of Kanturk and Newmarket are part of the Civil Parish and records there begin in 1821 and 1822 respectively, so you have a very good chance of locating further information.
You could try checking www.familysearch.org or www.rootsireland.ie, (the latter is a subscription site) for church baptisms, marriages and burials. As Civil Registration of Catholic births, marriages and deaths began in 1864 you should be able to locate a civil record on either of these sites; the marriage being particularly important as it should list the name of the bride and groom?s father and sometimes mother, thereby taking you back a further generation.
The 1901/1911 Census could also yield further information should you wish to research later years, if you find out for example, that John and Bridget did have children. You can access it for free here. http://www.census.nationalarchives.ie
There is a graveyard in Kanturk and according to the link below there are some transcriptions done for Clonfert Graveyard there, but there are no Hannon?s listed so far. There is also a graveyard in Newmarket and you could try checking the Historic Graves website for that, also linked below.
http://www.findagrave.com/cgi-bin/fg.cgi?page=gsr&GScid=2324517
http://historicgraves.com/graveyard/clonfert/co-clft
I wish you the best of luck. Happy St. Patrick?s Day
Clare Doyle
Genealogy Support
Ireland XO
