Glad to help.
In general, the original parish records remain with the parish, and the images now available online are based on microfilm images taken of the originals. At the above NLI link, in the top center there's a link called "About", which describes the process. Basically, in the 1950's and 1960's, the original registers were taken to Dublin and microfilmed, then returned to the parishes. In the 21st century, the images were digitized, to make them available online. Since the records belonged to the parishes, it was possible to collect the ones from Northern Ireland as well, despite the political separation which had occurred by then. This program was designed to supplement the civil records, which started in 1864. Since the civil records were known to be spotty for the early years, a cut-off of 1880 (sometimes 1881) was used for the microfilmed parish records, in an attempt not to miss anyone.
Some parishes have online records at NLI well back into the 1700's, but in general the further west one goes the later the records start. In some cases, it may be that the parishes were poorly funded or organized at first, and didn't start keeping records until later. Where there are gaps or no records at all, it may also be that the records were damaged or lost over time. After the microfilming program was carried out, some parishes did find additional registers which had not been sent for microfilming, and which are not in the NLI collection, although some additional parish records in the Dublin area were added in the 1990’s. For that reason, it's good to ask about that, if you can get through to someone at the parish who will check for you.
There are also cases (especially in more isolated western areas) where, while the parishes were being re-established, there may not have been a building in a given parish in which to hold Catholic mass or keep records. For that reason, if there is a nearby parish with older records, it may be worthwhile to search there as well, since people may have traveled to a nearby church for baptisms or marriages. The officiating priest will often have stated the name of the townland where the family lived (or in some cases just the parish), even if it wasn't in his parish, which can help you to confirm that you have the right people. In your case, two adjoining parishes have older record: Banagher, starting in 1848, and Donaghedy, starting in 1854, so you might try there. At the link I gave you for Cumber Upper, you can use the interactive map to move to those parishes.
