Two things:  first, the Brattle Theatre here in Cambridge, Mass. is
currently running a Monday night series called "Jazz in Noir."  They
include "Streetcar Named Desire" in it, not because it is noir, but
because, according to them, it is one of the first Hollywood studio
films to incorporate jazz into its soundtrack.  According to my memory
of the movie, at least some of the music would be potentially
diegetic.
  Second, there is an excellent essay about the use of music in
Fellini's "Le Notti di Cabiria," and the ambiguity of its source,
whether diegetic or not so.  For instance, once early in the second
sequence, concerning Cabiria's encounter with the matinee idol, the
music clearly seems to be extra-diegetic, then Cabiria begins to dance
to it.  Other times, a clear source within the film is shown (twice we
see Cabiria lying on her bed with a radio next to her) but the
soundtrack's music is much more clear than the diegetic source could
deliver.  The woman who wrote this essay (whose name escapes me at the
moment) delivers a convincing analysis of the contribution of this
ambiguity to the overall themes of the film.  Her essay is included in
Federico Fellini:  Essays in Criticism, edited by Peter Bondanella.
                                                Stephen Brophy