How about this.. we each just record basic songs (cover or original) on our own using whatever instrument we have, post them on some kind of file transfer site and link them here, then we each take someone else's song, add a part, and post it back on the site, and pretty soon we'll have a bunch of songs. Also, if possible, try to keep the individual parts in separate files to make the final songs easier to mix.
To start off, who knows of a good file transfer site? We would need to set up a shared account on the site so that we could all access it whenever we want.
P.S. To make the collaboration easier, include a note with the song's structure (how many bars of verse, chorus, etc. or time signature - as detailed as you're willing to get).