Hi,
Thanks for your message.
Have you tried looking in church records for information? Most Catholic records are held locally so you may need to write to the local parish priest for possible assistance. One website that you may find useful is the Irish Times where they give an overview of what records are available in specific parishes. It also shows you where copies of the records are available. For Achonry parish, follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Sligo&parish=Achonry&churchid=117
Unfortunately from this link you can see that records for the parish do not begin until 1878. However, in the19th century new Catholic parishes were created so starting dates can sometimes be misleading. Many parishes changed their geographical spread so you may find earlier records relating to your family in the records of adjoining parishes:
http://www.irishtimes.com/ancestor/browse/counties/rcmaps/sligorc.htm
Most surviving Church of Ireland records are still held by the local clergy, although some are in the National Archives of Ireland and others are in the Representative Church Body Library in Dublin. Here are their websites: http://www.nationalarchives.ie/ and http://ireland.anglican.org/about/42
Lists of these surviving registers can also be found at the National Library of Ireland.
It may be an idea to contact The SLigo Heritage and Genealogy Centre for possible assistance, however a fee may apply. Here is their email: heritagesligo@eircom.net
Please be patient - as our programme has only begun to rollout across the island of Ireland and volunteers in some areas may not yet be organized.
Kind regards,
Genealogy Support