Walker's Hibernian Magazine (WHM) from 1771 to 1812. It also includes as an appendix a list of births, marriages, and deaths for the years 1793 and 1794 from the Anthologia Hibernica.
Just under 30,000 entries are in this database, which was indexed by volunteers as one of Ancestry's World Archives Indexing Projects; as such, it is free to users.
The marriages from WHM are listed under both the husband's and the wife's surnames. This double listing optimizes your search capabilities because if you do not know one name, you can search under the other and find out what the spouse's name is.
Some issues of Walker’s Hibernian Magazine are available online on websites like the HathiTrust Digital Library and Google Books, and can sometimes be found in university and other libraries.