I'm sure you have the Griffith Valuation of 1853 but
here goes anyway:
John Thompson, Parish of Ardkill, Townland Collinstown,
Poor Law Union Edenberry, tenant of Arthur Smith
3c house, forge and garden
There is one other in the Parish of Naas, Nass West Townland. www.askaboutireland.ie
1824 Pigot's Directory:
John Thompson, Leixlip, Kildare Timber Merchant
Patrick Dignam, Leixlip, Baker
Leixlip, Kildare in 1824 was a market and posttown
8 mi. west of Dublin, 4 mi east of Maynooth and 11 mi.
north of Naas.
Co. Kildare belongs to an Irish History Foundation that has births and marriages but did not find Edenberry nor
the Parish Ardkill.
I googled thinking that the parish may have been amalgamated with another, changed names etc.
Lewis Topographical Dictionary: Has Ardkill as a parish in the barony of Carbery, 4 mi. east from Edenderry, Union of Carberg. Edenderry not Edenberry but it was used in GV. I double checked the spelling in Griffith Valuation.
The closest then is Leixlip and and the parish records only go back to 1844.So you should be able to get the births of the children of John Jr.
There are about 28 Thompson's in the telephone book for
Kildare, some Leixlip and Maynooth as well as others.
Might be worthwhile writing a few letters.
Local Libraries have 'local studies'. Heritage and Museum societies have journals of collected memorial inscriptions from gravestones.www.genealogy.nationalarchives.ie
for Tithes 1820-1839www.censusfinder.com
+ Kildare - look for archives and photo's rom gravestones