Claire, I don't think you will be able to find out anything further back on this woman unless you can provide a location and/or her father's name. Sometimes you just have to "bite the bullet" and go ahead to purchase a certificate. Even if it proves to be the wrong one, at least you will have ruled out that as a line of enquiry.
Have you looked at the Clare Library site? www.clarelibrary.ie
& go to the genealogy & family history section.
You may find references to Connors, but unless you know the fathers name you won't know if they are relevent or not.
Good luck with your searching!