Irish companies:
Businessworld Irish shares lists all Irish PLCS. From these pages you'll get links to the companies' sites which should host their recent annual reports.
International companies:
Many of these sites require user registration. You may only get access to current reports so you may be better off going directly to the company's website.
Large companies.
Normally you should be able to get recent annual reports from a publicly listed company without much difficulty. However, private companies are not subject to the same reporting requirements. So although some private companies may publish annual reports, many do not, and financial information may be difficult to retrieve.
Irish subsidiaries of multinational corporations.
Many companies in Ireland are subsidiaries of multinational corporations. Annual reports may only be available for the corporation as a whole, and financial information relating specifically to the Irish subsidiary may not be provided.
Smaller Irish companies.
Many smaller companies, especially if private, do not put annual reports or financial information on their web pages. Some do not have even have a website. In this instance you if you want financial or other information you'll probably need to contact the company directly.
I can't find older reports online.
Many companies put annual reports on websites for recent years only. So there is no guarantee that reliable, permanent archives will be built up over time.