There are Roman Catholic church records available for the diocese of Claregalway (Galway). These date from 1849 for baptismal, marriage and burial records. You can find these at the National Library of Ireland, Pos. 2429. If you have any difficulty, you could try writing to the parish priest for more assistance.
Could you please post your message on the County Mayo page here: http://www.irelandxo.com/group/county-mayo
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 they arrived at, this could be a good place to find more information, and perhaps even find out an exact place of origin.
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith'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. Tithe Applotment Books (1823-38). Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS).
You can information about the frequency of the name in the mid-19th century and any other variant spellings of the name here: http://www.irishtimes.com/ancestor/surname/
You could also check the book by the Claregalway Historical & Cultural Society, Claregalway parish history 750 years = Stair pharoiste Bhaile Chlair na Gaillimhe, 1999.
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.
Genealogist (Ireland XO)