It really depends on where they lived as to how to progress.. but since you have the two full names, at least you will know for certain if you find a match.
The place to try first is
www.irishgenealogy.ie This (free) website has records for some parts of Ireland ... Dublin City, parts of Co. Cork and City (RC only at the moment), Co. Kerry, Co. Carlow (Church of Ireland only) - more records are due to be added soon.
you could be lucky and find them there..
Other records for some parts of Ireland are available on the Irish Family History Foundation website
http://www.rootsireland.ie/ - but this is a pay-website
Shane