What's your budget?
I've had to do some research into this recently for work, and in the end we replaced our 200 iPod touches with small Galaxy tablets due to lack of viable budget options. I did find a company (think it was Motorola) that made a version of one of their starter phones with no SIM slot, this was the closest I could find to an android version of an iPod, but it wasn't cheap enough for the volume we wanted.
In fact, if your budget permits it there are quite a few premium options - Sony Walkmans are now Android-powered.
Ultimately an old smartphone might be worth a shout if you have one around, even without a SIM you can stick apps on it and stream music off wifi/internal storage.