I searched on the subscription site Roots Ireland and did not find a marriage record or baptismal records for children of John Kilkenny and Mary Dillon.
The 1833 Tithe listings showed a John Kilkenny in Killeen townland in Knock civil parish http://titheapplotmentbooks.nationalarchives.ie/reels/tab//004625688/004...
The Tithe listings were incomplete and we don't know if this is your John or not.
The 1855 Griffiths Valuation head of household listing for Co. Mayo showed six John Kilkenny records all in East Mayo parishes as follows:
Killeen townland Knock civil parish (likely the same person from 1833)
Lassany townland Bekan civil parish
Cloontumper townland Annagh civil parish
Falleighter townland Aghamore civil parish
Caher townland Aghamore civil parish
Carton North townland Aghamore civil parish.
We don't know if your John Kilkenny was still alive in 1855 and whether he was leasing land but the above are leads.
Have you considered a DNA test?
Let me know if you have any questions.