I was surprised to discover yesterday that everyone, not only local library members, can get full and free access to Nexis, the huge online archive of Irish, UK and international newspapers and journals, thanks to Libraries Northern Ireland.
I've spoken to Libraries NI to make sure this is intended, and not an access error that will be put right when we least expect it. And it is indeed correct.
It seems the current access arrangement will continue until March 2016 at least, and all you need to feast on the Nexis database are a user-id and password, which you can find on LibrariesNI's Newspapers page (note that the log in details may change every now and again).
Among the 40,000 sources in the database are the Irish Examiner, Belfast NewsLetter, Derry Journal, Ulster Star, Dromore Leader, Ballymena Times... You can find a full list here. The period of coverage varies by each source; for many it is the last 20 years.
Enjoy.