Thanks very much for the reply Nicky! (And yes, your site is working too)
Yes, I know about the commoness of the (O')Connor and Murphy surnames.

I gave up on Mary Murphy before I'd even started. I thought I might have a chance with Dennis Connor as Dennis is perhaps not quite so common as a first name?
I will look at the library site and the churches - thanks for those.
Now this you probably won't be able to assist with this, but my gg grandfather came from New Ross, born about 1863. Does your knowledge of the county cover that area well enough to know the church he may have been christened in? His name was Thomas Joseph Healy. I thought I'd struck gold when I discovered his parent's names - Darby Healy and Anastasia Ryan! But there even seem to be a couple of them around.
I recently did some thinking and wondered if the forenames I thought of as unusual - Darby and Dennis are possibly anglicised too. There are Irish versions of these names. And Anastasia isn't at all rare in Ireland ... never mind ...
If you ever come across these names or anyone researching them, please let me know.
Wexford looks like a lovely place - I sometimes wish my ancestors had stayed there

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PS. Have you thought about a Wexford surnames section for your website? Perhaps somewhere people could list the names they are searching for? Also a list of the most common names in Wexford?