Ask you OLDEST ancestors (family, uncles, aunts, etc) to find as many full names, associated DOB, DOM, DOD, as possible. Then use this info to find the family in the censuses going back decade by decade.
Eventually you will find beside one or more names that they were born in Ireland.
When you find this, then research the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
For this surname in the current database, there are 3,712 Kiely B rcds dating from 1752, and 1,607 B rcds dating from 1760. If you are industrious, you can probably trace your lineage back to the 1820s.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.