I have Barry's in my family tree that were from the Bandon area of County Cork. My great aunt told us that they came from Wales so I checked the 1861 Wales Census and found them there. I also found the name Bandon, Cork listed as the birthplace. My Barry's were also part of the 1851 Wales Census. There was a large community of Barry's that left Ireland to work in the coal mines of Glamorgan, Wales. Many of them left Wales to come to the U.S. during the 1860's.
Try looking in the 1861 Wales Census to see if your family is there.