You are leaving this a bit late for finding some background.
The easiest thing to do would be to send some letters ahead but there is no way there is enough time to respond to your requests.
The telephone book shows 21 Rellihan listed in Cork
8 Castleroche/Relihan 6
10 Mallow/Relihan 10
2 Macroom/Relian 2
2 Donaughmore/Relihan 2
1 Midleton/Relihan 1
Usually the telephone book requires EXACT spelling but no so sure in this case as the numbers are about the same.
There are 68 Parish's in West Cork, 110 in East Cork and 71 in N.W. Cork.
A little more information is required. Do you have any names and dates? There are two places to go to find records once you are there, there is a History Foundation located in Kildare that has the North-East portion of Cork and
a South-West genealogy office independant of the History Foundation.
If you are planning on visiting Parish's you should take the phone numbers of the Clergy and make appointments to see parish registers or have help with same. If you know the parishes you can visit ones where your ancestors lie
and take digital pictures (no sun if possible) or take rubbings on the ones too worn out to take a picture of.
Some white tissue paper used for wrapping gifts and a couple of black wax crayons do the job.www.corkandross.org/parishes