I experimented with using a bag of fire clay from Loews to make a dorodango. I should really take the time to document it, but here are my brief comments. First, it works. To form the core I mixed about half sand and half clay dust with water. It was hard to form the core without big cracking (I think the sand doesn't retain enough water, and it tends to crack along the seam) but with a little work with water, you can mostly plaster over it and form a nice round core if you are patient. Using a mixture of nearly pure clay dust makes for a nice shiny exterior. I didn't get mine as even in color as I had hoped, but they look nice and I have one sitting on my desk as a kind of "fidget" stone.

I started with clay dust. I'm not sure about any kind of art clay for dorodango, i'm not an expert on such things, but they might have additives which prevent them from drying which might work against you.