Unlike most searches at least you have Kilkenny as the county. A good start. There is a baptism and marriage
data base for Kilkenny www.rootsireland.ie
you should be able to find the parents names with at least one of the names, it is a paywebsite but that is common in irish ancestry. I note most of the Parish's start about 1820 give or 5+/- years you might be lucky. Start with the unusual names first, Lawrence & Matthew, William, Thomas and Edward
A baptism record comes with a father and mother's name and mother's maiden name, address/parish and date. Once you have the parents names you should be able to find all of their children.
If parents lived past 1864 which is the time of registration you can look them up on www.familysearch.org
There were no Lawrence or Mathew Fanning's in the 1849 Griffith Valuation used as a census substitute out of 64 Fannings.
3 x Thomas in Dunkitt Parish
1 Dysartmoon Parish
William Parish Burchurch & Tiscoffin
Edward x 2 in Parish Kells
The majority (90%)of Irish were tenant farmers.www.genealogy.nationalarchives.ie
has the Tithe Applotments from 1823-1837 (census substitute)
William Fanning, Parish St. Maul's
Thomas Fanning, Parish Callan & another Parish Dysartmoon www.igp-web.com
+ Kilkenny (once you know father's name there maybe gravestone inscriptions)
There are 8 Fannings in the current on line telephone book for Kilkenny and once you know the area your family came from you can contact them. Or, as I would do is write all 8
in the off chance someone would be able to help you.