Hi Roger,
Thank you so much for your reply and the sources that you have provided. Unfortunately, the younger Michael Haran their son was in England at least by 1896 and we already have him on the 1901 census living with his wife and family in Stockton. Ancestry.co.uk - 1901 England Census. In response to your question, we have Michael's marriage index to Ellen Costello in 1896 which is also in Stockton in England.Ancestry.co.uk - England & Wales, Civil Registration Marriage Index, 1837-1915
So this means that Michael Haran & Mary King's son Michael wasn't in Ireland in 1901 or 1911, so the records you have recommended us for the family in Cuillan, Kilconduff must be a different family. It's quite frustrating because we found the elder Michael Haran's 1900 death record just a few days ago and thought we had finally found them, because Cloonlara and Cuillan are very close on Google Maps and all the information seemed to fit, but then we found the 1901 census follow up of the family and discovered that it couldn't be our ancestors!
Unfortunately, this means that none of the records you suggested can match our information, however, we didn't know that you could find records on the website Irish Genealogy so thank you very much for reccomending that to us. We are very excited about it and have already found the younger Michael's birth certificate image - we only had a transcription beforehand.
We will continue to keep searching and thank you for your help and quick reply.
Best Wishes,
Georgina