Hi Kim,
Do you have any idea about what part of County Cork they were from? Cork is a very large county with many, many parishes. So the first thing you will need to do, is to try to narrow down the place of origin from County Cork to a parish in Cork.
There are some documents you could try checking to help narrow this down. When you do find out where in Cork they were from, then I can recommend some church records for you.
You could try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffth's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at. Many of these are records particular to Cork.
Civil registration records are available from the General Register Office (GRO). These start from 1864 however. You can access the website here: http://www.groireland.ie/research.htm
Have you tried checking the Ellis Island records (www.ellisisland.org) or the Castle Garden records (www.castlegarden.org)? Generally, more information was given at the port of arrival rather than the port of departure. If you knew which city James arrived at, this could be a good place to find more information, and perhaps even find out an exact place of origin.
You could try checking local newspaper obituaries for possible clues about their place of origin. They may point to a more specific place in Cork.
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Kind regards,
Sinead Cooney
Genealogist (Ireland XO)