Hi Elizabeth,
I can understand why they tell you that there is too many Mary Carney to determine which was yours due to the fact the Indexes only show name and district they were born in without any parents' name.
In order to do it, they HAVE to go all through the birth entries which is too much work for just one pound.
If you want to purchase the transcription of her birth entry, they will oblige you with it. Or you can always send for the photocopy of her birth entry at the
www.groireland.ie since you have her parents' names and county and year.
They will do it for you only 6 euros.
Or applying to the
www.groni.gov.uk for tenner and 50p for a certified copy online and they will get it to you within 10 days as opposed to the Irish GRO which will take about 4 weeks.
Another website for you to try is:
www.ancestryireland.com and they have a database of mixed civil & church records. There is a good chance your Mary is there.
Kind regards,
Tees