There are Rainsfords still living in Murroe and Doon, nearby (where there was a Rainsford Grocery, now closed). Some claim to be different lines than "mine" but I wonder if they are connected further back. I met a wonderful lady, Sara Rainsford, who is connected to my family, about 5 years ago, who has since passed away. She lived down the road from Annagh, in Cappanahanagh, also in Murroe. There is also a researcher of Rainsfords from this area in Ireland in the US, and I could connect you. "His" Rainsfords lived near Newport, Tipperary, just "up" the road.
I have never found my Mary Rainsford's family, so would be glad to share what I have. My email: firstname.lastname@example.org