Of the many, many musical references that Joyce uses 
in Ulysses, there are some that are quite significant 
and some that are only briefly alluded to. One of the 
more significant references, though it's appearance is 
much more concise than songs like The Croppy Boy and 
Love's Old Sweet Song is the traditional Irish song 
Suil a Run. It is used in the Ithaca chapter. Chapter 
17 of Ulysses (Ithaca) is written entirely in question 
and answer form, like a catechism. 
At one point as Stephen and Bloom walk back to Bloom's 
house, they each refer to one song, which represents 
their culture. Bloom picks a Hebrew song with which I 
am unfamiliar. Stephen chooses a song which tells of a 
young woman who is pining for her lover, who has fled to 
France. If you don't have your copy of Ulysses handy, you 
can find this portion on the internet 
here. But this 
particular question and answer are below:
"What fragments of verse from the ancient Hebrew and ancient
Irish languages were cited with modulations of voice and 
translation of texts by guest to host and by host to guest?
By Stephen: suil, suil, suil arun, suil go siocair agus suil 
go cuin (walk, walk, walk your way, walk in safety, walk with 
care). By Bloom: kifeloch, harimon rakatejch m'baad l'zamatejch 
(thy temple amid thy hair is as a slice of pomegranate). "
There are many recordings of Suil a Run. The best is on the 
album All of It by the band Skylark. Instrumentally, the song 
is simple and perfect and no one sings it as beautifully as 
Len Graham does in this recording. 
Suil Arun (the spelling 
varies) is also a song from Joyce's personal repertoire. Listen 
to it if you get the chance. The link above provides a sample 
of the song.