The family may be difficult to trace. Assuming they lived in Clogher, there are no baptism records for that RC parish earlier than 1855 which, according to a post you have put on another board, is when their last child Owen was born. He does not appear top be in the 1855 baptisms.
There’s 1 Bernard Daly in Griffiths in Clogher parish but he remains in the area till the 1880s, so is presumably a different family.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society are running an Ulster DNA project and can offer FTDNA testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).