I am related to more than one Reidy/Ready family from the Chemung County, NY area, but I cannot link them to yours. These were all very common names, so without something truly unique, it's hard to connect the people through names!

Michael T. Reidy (b. September 10, 1826) m. Bridget Kane (b. 1839ish). I have more than one report of origins in Co. Clare, but little hard evidence. They sailed to NYC on the Lucy Thompson arriving on June 18, 1863. They settled in Horseheads, Chemung Co. NY.

Margaret Reidy m. John Ryan (b. 1835ish). They resided in Bangor, ME, prior to coming to Elmira, Chemung Co., NY. Their daughter, Hannah (b. May 15, 1859) married Michael Kane. They resided in Elmira, NY. No known connection to Co. Clare, but reportedly a familial connection to the next family...

Mary Ready (b. August 19, 1849) married Patrick Thomas Ryan (b. 1847ish). They hailed from Liscannor Parish, Co. Clare, Ireland.