Parish of Conn might be Conna, and unfortunately I do not have my reference materials in front of me but I think that is up towards Mallow (north end of Cork). You can check Mallow Heritage Centre.
I am assuming your Briens were RC. The union of Skibbereen in 1840 also included the unions of Skull and Clonakilty and did not become separate unions until later. You can search http://irishgenealogy.ie
in the relevant RC parishes (Skibbereen, Rath & Islands, Rosscarbery, Clonakilty, etc). NOT ALL remaining available records are online yet, but are due to come online some time this year.
Getting started (has links to maps of parishes and much more):http://www.corkgen.org/publicgenealogy/cork/genealogy.html