Dwight Radford posted a blog this week on Irish Newspaper Databases. One of the databases he mentions is Irish Newspaper Archives. This is a bit pricey…an annual subscription is €350 ($430), however they do have a 24 or 48 hour subscription for €10 - €15. This database is available also at the National Library of Ireland (for in library use only) and is where I found the obituary of my husband's great grandmother last month. Although she died in 1935, her death is not listed in either the FamilySearch Irish Civil Registration Index, nor in the Indexes at the General Register Office and I'd been looking for this information for years. I was defininetly doing the happy dance!
The second database mentioned is the British Newspaper Archive which also contains newspapers for Ireland. This also has a hefty price tag for a subscription, however you can register (for free) and purchase credits for 2 days (£6.95) or 7 days (£9.95). Once registered you can search and see what is available before you decide to purchase credits.
Newspaper Archive, a U.S. newspaper database, also has a number of newspapers listed for Dublin, Ireland. Their subscription rates vary from $5.99 - $9.99 a month depending on the length of your subscription.
I would also add to Dwight's list GenealogyBank. They have a section on Irish American Newspapers which frequently list events that occurred in Ireland, including death and probate notices.
The digitization of additional newspapers is going on constantly, so it's always good to check back and see what's new. But remember, not all newspapers are digitized, especially those from the small towns where your ancestors lived. You should always check for microfilm of local papers both here and abroad when your traveling. Although not as easy to use, since you can't search, knowing an event date can lead you to an article on the event. So don't forget to check newspaper databases as well as local newspaper microfilms in your research.