Hi there,
Cork is a very big county! Without a definite idea it is very difficult to direct you to church records etc. However, you mention Dunamanway. The Roman Catholic church records for this parish start from 1818 for baptismal and marriage records. These are available at the National Library of Ireland, Pos. 4805. If you have any difficulty, you could try writing to the parish priest for more assistance.
You could also 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.
The Failte Romhat website has lots a links and information specifically for County Cork, so you should look into these.
If you know anything about their emigration, then you should check the sources in the US and Wales. Generally, information was given at the port of arrival rather than the port of departure.
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)