Thank you for your post to the Ireland Reaching Out message board and welcome to the site!
We have a Bergin volunteer who might be interested in your post and I will forward it accordingly.
If you are not aware, the Clare Library has a lot of wonderful online resources that you might find worthwhile. Their link is below:
In addition, the parish registers for Bunratty are available online through the National Library of Ireland website:
You will note that the Catholic Parish name is Newmarket-on-Fergus.
You might note that there are Church of Ireland registers which fall under both names of Kilnasoolagh and Kilfinaghty. Ancestry has some years of these registers and others (older) are held at the RCB Library in Dublin.
If you need further information, please let us know.