Hi,
Thank you for your message.
Do you know much about their emigration? The dates, the reason why they left, who they may have travelled with?..etc..Generally more information was given at the port of arrival rather than the port of departure. If you knew which city they arrived at (e.g. Liverpool, New York, etc.), this could be a good place to find more information.
You could try checking the land records called the Tithe Applotment Books (1823-38) http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp or the later Griffith's Valuation (1848-64) http://www.askaboutireland.ie/griffith-valuation/ or the Church of Latter Day Saints (LDS) https://familysearch.org/ for memebrs of their respective families.
You might also try:
British parliamentary papers on Ireland can be found at: http://eppi.dippam.ac.uk/documents/9824/eppi_pages/215093
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 National Archives UK ? genealogy search: http://www.nationalarchives.gov.uk/records/looking-for-person/
The Library & Archives of Canada - http://www.collectionscanada.gc.ca/index-e.html
Remember to post as much information as you can with regard to the people you are researching. The more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.
Kind regards,
Genealogy Support