Hi John
I'm sure I had already sent you this info but maybe I was having a senior moment.
Anthony Kilkenny lived with his wife Ann Charles at Tooma, parish of Cloone (RC parish of Aughavas). There is no record of their marriage in that RC parish but these are often absent from the records; either the record was omitted or the couple married in another parish. There were several Kilkennys in Tooma and I see no reason why that townland could not have been his home/place of birth.
In 1901 I believe his son John held the land and with him was his widowed mother aged 70. Assuming Anthony was of a similar age we would not find a birth as Aughavas records only start in 1843.
The first son I can find was Patrick in 1861 and, if he was indeed the first son, this could well point to Anthony's father also being Patrick.
As to further work I suggest you contact the Land Valuation Office in Dublin. If you give the name Kilkenny and the townland of Tooma you can purchase from them a list of how land changed hands between Griffith';s Valuation and the early 20th century. You should be able to see who passed the land onto Anthony and who he in turn passed it on to.
Best of luck
Jim