If it's contemporary music scores and sound recordings you're after, you will more than likely find yourself visiting the wonderful Contemporary Music Centre beside Handel's Hotel on Fishamble Street. Housing over 10,000 works and more than 9,000 recordings, as well as books, journal holdings, and concert ephemera (CMC, 2017), the CMC Library and Archive is a public library. Its collections are for reference only, but you can buy many of the scores, books, and CDs from the CMC shop. It is worth noting that many of the works by 20th- and 21st century Irish composers in the CMC Library and Archive are completely unique - this is the only place you will find them.
You can do a simple search for specific works by title, sub-category, or composer here, however if your query is more complex, you should email Library Coordinator Susan Brodigan at firstname.lastname@example.org to arrange an appointment. With her brilliant expertise, she can help with repertoire queries, musicology research, and she can even suggest pieces for performance.
The CMC compliments, and is complimented by, the Irish Traditional Music Archive (ITMA) with very little overlap in holdings.