clm, I'm not quite clear what you're looking for here. A lot of traditional songs and ballads are mentioned or quoted in Ulysses, as well as many popular and art songs. I don't know what you mean by "the library of pub songs"; but I am sure some Joycean scholar has managed to compile a list of the songs in Ulysses, which ought to be available in any good academic library. If you can get your hands on such a book, and then want to know something more about the songs then there are probably some people here who could help. If you have some particular songs already in mind, and would like help with those do let us know.
There is somewhere in the book an interesting discussion between Bloom and Stephen of that appalling ballad The Jew's Daughter.