Historian Brett Holman has a list of British newspaper archives available online at his blog airminded.org. Included within it are a good number of titles from Ireland and Northern Ireland:
- The Anglo-Celt (Cavan)
- Belfast Gazette (free)
- Butte Independent 1910 to 1930
- Connacht Tribune (Galway) from 1909
- Connaught Telegraph (Castlebar)
- Donegal News
- Evening Telegraph (Dublin) 1901
- The Freeman’s Journal (Dublin) to 1924
- Irish Independent (Dublin) from 1905
- Irish Times (Dublin)
- The Kerryman (Tralee) from 1904
- Kildare Observer (Naas) to 1935 (free)
- Leitrim Observer (Carrick-on-Shannon) from 1904
- Limerick Leader from 1905
- Longford Leader
- Meath Chronicle (Navan)
- Munster Express (Waterford) from 1908
- Nenagh Guardian
- Nenagh News to 1924
- Southern Star (Skibbereen)
- Sunday Independent (Dublin) from 1906
- Tuam Herald
- Ulster Herald (Omagh)
- Westmeath Examiner (Mullinagar)
Click here to access the full, hyper-linked list. Note, though, that most of them require you to pay to get access to them.
Irish and Northern Irish newspaper archives online by Bruce Gaston