Counkilla or Ceancullig (Gaelic: Ceann Coille) is located just north of Drimoleague. It is a townland in Drimoleague parish. Clearly there are numerous spelling variations of this place that you may find, some more phonetic, some more true to its Gaelic origin.
See the entry for Ceancullig on Townlands.ie for more information about this location.
Historic maps for this area are freely viewable on the Ordinance Survey Ireland website. On the maps I viewed the name is spelled Ceancullig.