Hi Dan,
Making your own clay paint sounds pretty permie to me.
You're probably looking for basic "bagged, powdered, fine clay" but what it's called where you are may be different to me here in the UK.
Maybe let people know where you are so you can get some local advice.
Here's a link just for inspiration:
Clay-Works Finishes
I have prepared my own clay from local sources before - for sculpture not paint-making - and it is quite time-consuming so even if you had some locally it does not sound like it would be an option if you need to do this quickly.
Good luck with your project.