James & Thomas’s births are well before the start of statutory birth registration in Ireland (1864) so you would need to rely on church records to trace them. You haven’t said what denomination they were. The majority in the 1901 Irish census appear to have been RC. I checked the on-line RC baptism records but did not find any that might be Thomas. It’s possible he came from a parish that doesn’t have any records back as far as the 1840s.
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).