My favourite Irish female singer from the 1960's is Anne Byrne. I live in California and actually found one used LP by Anne Byrne in a record shop here many years ago but was lucky to find more when I visited London in the 1980's. There were some great record shops in London and I found more Anne Byrne albums then. Also another Irish singer I liked was Jane Cassidy and bought two of her Lps when I visited Dublin, Ireland in 1983.
I have listened to other Irish singers from the 1960's but Anne Byrne by far is my favourite.