I think the townland that Charles Caldwell lived in was probably called Cloonarell (not Cloonare). Griffiths Valuation for 1857 records a person of that name renting a farmhouse, outbuildings and a total of 32 acres of land (plots 5 & 6) in Cloonarell. That’s about a mile from Killygordon and would be easy enough to locate today, should you ever wish to do so.
The family had left the townland by the time of the 1901 census. To find out exactly when they left you would need to consult the re-valuation records in the Valuation Office in Dublin. (These are not on-line).
William’s birth is long before the start of statutory birth registration in Ireland (1864) so you won’t find a birth certificate for him but you might find his baptism, and that of any siblings, if you know his exact denomination. If he was Presbyterian then the local baptism records start in 1821. If he was Church of Ireland they start in 1802. Copies of both sets are held in PRONI (the Public Record Office), Belfast but are not on-line anywhere as far as I am aware.