Hi,
Thank you for your message.
Have you tried using the land records pertaining to Ireland in the 19th century? Although these do not have any genealogical information in them they can be used to tie individuals to specific places. You could try searching for James? parents in these and also James himself. There are two:
The Tithe Applotment Books (1823-1838) found at http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
and Griffith?s Valuation (1848-1864) found at http://www.askaboutireland.ie/griffith-valuation/
Once you have a definite parish, you can then check Church records for information. Most Catholic records are held locally. One website which you may find useful is the Irish Times. Here they give an overview of what records are available in specific parishes. Follow this link to maps of Galway Roman Catholic parishes. Just click on the relevant parish and you can see what records are available there:
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/galwayrc.htm
For Church of Ireland records check http://ireland.anglican.org/about/42 and http://www.nationalarchives.ie/. The Anglican Record Project is has created an index to their records: http://ireland.anglican.org/cmsfiles/pdf/AboutUs/library/AngRecord/bunclodyunionindex.pdf
You could also try looking into his emigration. Generally more information was given at the port of arrival rather than that of departure. For information on immigration records in the US check the US National Archives at the following link:
http://www.archives.gov/research/immigration/
You should also be aware that there are many different variations on McCue that could have been used. Here is a link to that shows some of these variations and gives some information on the surname:
http://www.irishtimes.com/ancestor/surname/index.cfm?fuseaction=Go.&Surname=McCue&UserID=
Some other websites which you may find useful in your research are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Genealogy links: http://www.genealogylinks.net/uk/ireland/galway/index.html
Family Search: https://familysearch.org/
CENSUS RECORDS There is lots of useful information to be found in the 1901 and 1911 census records. You can find this here: http://www.census.nationalarchives.ie/search/
I hope that this is helpful. Best of luck with your research.
Kind regards,
Genealogy Support