The Tithe Applotments are the earliest census substitute available for Ireland. The next census substitute is the Griffith Valuation of 1858 in Sligo.
77 Kaveny, Keveny, Keaveny, Caveney,
Neither of the above names in the Parish of Emlaghfad, or the Townland or Town of Ballymote
There are baptism and marriage records available on line for Emlefad & Kilmorgan
Church of Ireland baptisms 1762-1921, marriages 1762-1895, deaths 1762-1893
RC Parish baptisms 1856-1899, marriages 1824-1899
Thomas and Mary would of been married before his transportation and unlikely to have been in the marriages of 1824+. A marriage record would of given you Thomas and Mary's father's names.
They would likely have married in Mary's parish if different from Thomas.
Their children's names should give you a clue as to parents names. lst. son name after father Thomas but if not the name would be his father's fathers name, 2nd. son would be named after Mary's father.
The telephone directory for Sligo, has no Kavanagh/Cavanagh's - other counties only
Keveny in Castletown, Easky
Keaveny, Killeen Dromahair
None for other spellings, the phone book is spelling specific.
I would try writing the two Keveny & Keaveny, addresses given in the phone book are sufficient for mail delivery and no postal codes required. Nothing to lose.
A company which has an expensive membership fee has gravestone inscriptions and in 1900 there was a survey of Emlafad graveyard. That doesn't mean there was a gravestone to read. Any gravestones for my husband's family are unreadable after 200 years.