Your message here is quite old so I hope you are still researching the Connaire surname. My gr gr grandmother was Bridget Coniry married to Patrick Brown. There are multiple spellings for her surname, with Coniry being the most common on all of the children's birth records. Bridget Coniry was born about 1838 according to the 1901 census. They were from Cloughoola, Marble Hill, Galway in the parish of Balynakill. I have their death records from that location. Most of the children emigrated to Lowell, MA but one daughter, Catherine, married a Michael Holleran and they lived in Lagoo. As far as I can tell from census records Catherine and Michael had at least two sons and 3 daughters. I haven't been able to trace Patrick or Bridget back further, but have quite a lot of information going forward. It seems there is a chance that our Connaire's are connected.