Have you tried https://www.familysearch.org? While you do need to register, it is free to use.
P.S. I am currently resident in the US, but am from Australia, and have done much research online for Wales, Ireland, Scotland, England, Australia (because I am not able to physically go to the libraries and archives as I used to when living back Home) and Sweden (and was pointed where to get access to records by some lovely Wikitreers), as well as some parts of the US (although I suck at US research).
Another good place to look for Ireland records is https://churchrecords.irishgenealogy.ie/
