Well that's depend a bit on what you call a song. I would personnaly include in the list tragedy fragment, or prayers who were sung. Another problem is that there were no titles at he time so most of them are still known by their papyrus name, which is clearly less attractive that the song of Seikilos. But some were copied and were found in Byzantine manuscripts, but most of the time the musical annotations, rarely known by the copists were not added. In fact I searched extensively for those kind of music and made myself a personnal playlist of ancient greek music. Annie Bélis is reknowned in this field, you can watch this lecture (in french): http://www.dailymotion.com/video/xe0gxi_annie-belis-reecouter-la-musique-gr_music

The titles:

Mesomedes of Crete made some hymns:

Hymn to Nemesis

Hymn to the Sun

Hymn to the Muse

Invocation of Calliope and Apollo

So what else: Some fragments of Poets contained musical annotations:

Pindar, the Pythic ode

Orestes

Euripides

some Papyrus name:

Berlin 6870 contains a Pean

Anonymi Bellerman contain some musical melodies (at least one of them is in the musics of the Rome Total war mod Europa barbarorum)

Some papyrus come from Oxyrynchus, a city in Egypt swallowed by the desert, which preserved the papyrus, there a probably more musical papyrus that waits to be read. I have more papyrus numbers, but without the sound, it's quite boring...

Fun fact: The first delphian hymn to Apollo was used in an instrumental version in Civilization III