We prefer private B&B's if they're available. Is that possible? Is there a site out there that lists them?
If you happen to go to Kilkenny, here's one we enjoyed in 2019, and our daughter enjoyed in 2023.. Katherine was wonderful.
I'm not sure what "private" means. Booking.com lists innumerable B&Bs - sometimes they are the cheapest rate, but it's worth googling to see if a specific B&B has their own webpage with a booking function. You can also look at Google Maps and search for Nearby/hotels and examine all the little red dots, which may only have a telephone number or email. I've resorted to walking the streets in Streetview (Google Maps) looking for signs on homes that include contact info of some sort. Some owners understandably refuse to pay the fees involved with booking websites, and you have to dig a little.