Hi Frances,
Thank you for your message.
Have you tried looking for Michael and Catherine's marriage certificate? This would give you definite dates of births. Sometimes marriage records can also contain more information such as occupations, residences or father's names.
Most Catholic records are held locally. One website which may be helpful is the irishtimes where they give an overview of what records are available in specific parishes. For Bekan parish follow this link:
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Mayo&parish=Bekan&churchid=1050
For Church of Ireland records check http://ireland.anglican.org/about/42 and http://www.nationalarchives.ie/.
Perhaps you could also try putting a message in a more local forum as their children were living in the 20th century, so this may increase the chances that someone who recognises the family name will make a connection with you. You could possibly do this here:
The Mayo Advertiser: http://www.advertiser.ie/mayo
The Connaught Tribune: http://www.galwaynews.ie/connachttribune
Some other websites which you may find helpful 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
Family Search: https://familysearch.org/
Genealogy Links http://www.genealogylinks.net/uk/ireland/mayo/index.html
I hope that this is helpful. Best of luck with your research.
Kind regards,
Genealogy Support
