I, too, am wondering what kind of Irish studies you are referring to. I have a set of CD's from an Irish "folk festival" which has nonstop (in my opinion) country & western sounding stuff on it. I would never use that as a listening example. Yes, "Danny Boy" (oy!) is an American song, lyrics written in the USA--like so much other "Aarrsh" music like Sweet Rosie O'Grady etc., is actually Irish American. What about the fact that some of the most "traditional" Irish Music is Harp Music? O'Carolan for example, wrote lovely tunes is still quite popular in jamming circles-- though he is sometimes considered one of the lesser talents of Irish Harp composers. There are some marvelous recordings of Irish Harp Music out there, & if you are looking for "Traditional" the above mentioned "Chieftans" have Harp & lots of other wonderful Music examples. The typical Irish Air is always lovely, & "Down By the Sally Gardens" is also representative of Yeats, as he penned the lyrics used for that Air when sung.
    I might also suggest that you consider doing as did my sainted Music History Professor taught us, play music as the students are entering the classroom. This can set the mood, & give lovely examples of Music at the same time. Hopefully they will listen & not make alot of racket.