The Irish treaty series is included on the Department of Foriegn Affairs and Trade page, and this is a very good place to start your search. This database has numerous treaties available, dating from 1930, and you can access the full text of the treaty from this website.
As Ireland is a member of the UN, European Union and is a signatory to the European Convention of Human Rights you may be able to get the text of treaties directly from these organisation. If you are having problems finding a treaty on the Department of Foreign Affairs and Trade site, it is worth going to the organisation that produced the treaty. The Irish website provides links to these in its left hand column.