The tithe applotment records for Coolnaleen in 1823 list a William Kavanagh with 9 acres of land. Likely to be a relation to Patrick K. (Possibly his father). They also list a John Walshe and a Thomas Wallis (which may be a variation on Walshe).
I think William may have been Patrick's father. Patrick's oldest child Margaret was born in 1842 so I'm assuming that he himself would have been about 20 in 1822. James was born in 1848.
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
Griffiths Valuation for 1850 lists Patrick Kavanagh in Coolnaleen. He had a farmhouse, outbuildings and 12 acres of land (plot 5) which, today, is just off the modern Crutt Rd. Should be easy enough to locate today.
There was also a James Walsh with land only (no house) in that townland. A relation of Judith’s perhaps?
Judith's father was James Walsh but do not know her mother's name.
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/
In 1901 there were 10 households there, including one Kavanagh, who is presumably a descendant of Patrick.
http://www.census.nationalarchives.ie/pages/1901/Kilkenny/Castlecomer/Coolnaleen/1459136/
This might be the widow of one of James' brothers, John or William.
Castlecomer RC parish records start in 1812, so you should be able to use them to build up a full picture of the Kavanagh family. Rootsireland has a copy of the parish records on their site (pay to view). Searching for children to Patrick Kavanagh & Judith Walsh born 1850 plus or minus 20 years brings up 7 matches. There’s a James Kavanagh birth/baptism to those parents in 1848. Don’t know if that fits with your information.
http://www.rootsireland.ie/