Hello @Matthew_Nutt,
From what I could find, Shariport should work as expected on the DietPi platform, although might have to do some manual configuration for it to work.
This thread should give you a starting point, although I cannot comment on exact steps needed to get this setup and working. If you are still having issues after looking over the thread, this might best be a question to post in the linux area of our forum.
Thanks,
Noris