I have a connection to you. My GG GM was Catherine "Kitty" Tuffy, who married Patrick Murray.
It has been challenging finding any info on the Tuffy family. One thing I have found...some of the Conway's were actually Conmy's. Hopefully that will be helpful. Also, I got a great deal of information by scanning the photos of the grave markers on IrishGraves.com
Please keep me posted if you find anything new and interesting.
Erin O'Hara Patrick