finale can print them, but can only play them back by using the pitch bend tool, and you have to program an invisible expression or articulation to turn it on, and then another one to turn it off on the next note.
and its has a problem anyway:
like if you had one instrument playing an F 1/2# and an A, the pitch bend would affect both notes, not just the F 1/2#
(unless... you put the second note in a second layer and have that layer play back to a different channel... but its messy)
sibelius makes quarter tones much more accessible to type, and it comes with a quarter tone playback plug in...
but i think it might have the same problem as finale with two notes in one part.
they both playback with midi, and midi assumes 12 equal tempered chromatic notes.
you could use a plain synthesis program like Csound.
doesnt type notation, just lets you write by listing frequencies and durations.
or you could just... get a violin.