Hmm, in my own research i've done i've found 4 possible origins of the name Corey. Ireland, Norman, Scot and English. All i know is that my direct ancestor, William Corey, immigrated from Bristol, England in 1634 to Rhode Island. In my family it has been handed down that my family comes from clan MacQuarry from the Isle of Ulva in the Hebrides. My Tudor-Stuart England teacher said that if William had been a tinker it is completely possible for a Scottish origin, especially since i know that William was a carpenter. My medieval england teacher said she thinks the name is Gaelic, but is not sure. Anyway, that is where i have landed in my own research.
What you said about the name originating in County Cork, Ireland is interesting. I do know that a MacQuarry emigrated to Ireland and founded the powerful Clan McGuire and i wonder if there is some kind of relationship.