There are Roman Catholic church records available for the diocese of Kilkerrin and Clonberne (Tuam), but these only date from 1884 which is too late for you. You might still like to check them for other family members. Baptismal records date from 1892 and marriage records from 1884. These unfortunately, have not been microfilmed by the National Library of Ireland. They are available from the Church of Latter Day Saints. They also have burial records dating from 1920-26. The ref. no. is 1279213 item 8-9. If you have any difficulty, you could try writing to the parish priest for more assistance.
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 This is also a little late in date for you!
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64) (which I see you have done already). 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.
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.
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)