Reidy/Kain (Kean) families

I am searching my 3x great grandparents Micheal Reidy (Reedy) and Bridget Kain (Kean - daughter of Patrick Kain / Keane / Cain and Bridget Meade, and who is the sister of Simon Kane) of Co Clare Ireland. They had two daughters born in Co Clare, Margaret, baptized in 1862 in Glaun, Kilmaley Clare. They then appear in Chemung county New York USA in 1865 where the rest of their 10 children are born and raised. I am descended through their first child Mary Reidy born 1861) who marries Thomas Mullin in Chemung county New York. If anyone has any information regarding these families or individuals I would greatly appreciate it!