After researching for over 20 years, I find the probability of Barnabas being born in County Cork, Ireland or Cork, Ireland in particular as being very unlikely at best. This input comes from genetic genealogy and genealogy researchers giving general feedback to my inquires.
My Y-DNA research began at Foulis Castle in the Highlands of Scotland, home of Clan Munro. After staying at Foulis over several days and discussing the subject with the Clan Chieftain's mother and chief historian at the time, I joined the Clan Munro DNA Project at Family Tree. Experts in the field of genetic genealogy research at Family Tree in the addition to my own research has my line of Monroe Y-DNA coming from the southeast area of County Cavan, Ireland. Historically, there have been Monroe families coming and going over the last 200 years. I have located several Monroe Y-DNA matches over the years with half of them sharing the common ancestor Moses Monroe Sr., son of Barnabas b.1722. The other half of my matches appear to be in the generations before Barnabas. One unique match is a McEnroe which appears right in the middle of my Monroe matches.
McEnroe is a family line more heavily concentrated in the southeast area of County Cavan, Ireland. So much so, one deep researcher of the area strongly believes the my line of Monroe was originally McEnroe with the spelling change originating with an event of someone changing the spelling to match the more familiar Monroe from McEnroe as was a common practice up to 100 years ago. I plan to work with the matching McEnroe individual to urge him into taking some deeper DNA tests to see exactly where he fits into our DNA tree.
So, with this information at hand, I plan to focus my evaluation of published online family trees giving a higher priority to the birth location of Barnabas or generations before him in the Counties of Cavan or Meath, Ireland. Lowest priority will be a birth site of County Cork, Ireland.