The Sligo Observer was a short-lived weekly newspaper published in Castle Street from 1828 to 1831. I'm not sure of the precise dates, but the BNA holding already has all editions from 9 October 1828 to 10 February 1831, so this may now be complete. The Leinster Independent was published in Portlaoise. According to its masthead, it covered Kildare, Kings, Queen' and the Midland counties. Just 24 editions from the first six months of 1872 are available so far, but the BNA plans to include editions from 1869-72. The paper published the usual fare of political, royal and British army news, but was also keen on sport and social news. It also reported with some enthusiasm on petty and quarter sessions reports of trials regarding violent crimes, some of them from other parts or Ireland, and even the UK or France when the crime was bloody or sufficiently salacious.
Both papers have also joined FindMyPast's Irish newspaper collection, which is included within a World or Ireland subscription package.