I am thinking about straw, pine shavings and horse pellets. This is very expensive stuff. A bale of straw cost around $23 - $25 and pine shaving cost even more. I will have a look at horse pellets.I put down lots of straw, pine shavings, and horse pellets (that turn to sawdust). Like every few hours would need another layer of bedding, because the previous layer got soaked through. When the weather finally dries, I rake it out, let it dry, and store it away to reuse. Do you have a roof on your run?
A bale of sugar cane cost around $12. I have 3 chicken runs.
1/3 of the chicken run is under cover, the rest has mesh to stop wild birds from entering the chicken area. This is the kind of mesh that to put on fruit tree.
If I cover the whole of the chicken run it still would not make any different because the rain is flashing into the run in all direction.