It turns out that there is something you can buy called BioFoam Beads and they are plant based and compostable, but they are probably also expensive.
It also turns out, from my research, that they are called bean bag chairs because they were originally filled with beans.
And I found another site that recommended any of these things as well: Popcorn kernels, rice, buckwheat hulls, dry beans, cedarwood shavings.