Cathy,
This is a very difficult area to research when all you have are the surnames of McElliott and Corcoran. The Irish census in the main were detroyed by fire in 1922 however the best place to commence is with the Griffith's Valuation of 1848-1864(just Google it). During this time there were no McElliotts in County Cork and only one in all of Ireland and that was in Co. Kerry. With Corcoran however there are many in Co. Cork.
Do you have any further information?
John...Sydney