We have a similar set up. I use a large "under bed" storage container. I have been filling it with 1/2 peat moss, 1/4 sand, 1/4 dirt & last 1/4 DI earth & ash. We then stick it in the back corner by wheels are and support it. Its supported with wood frame(2x4) on the bottom. So when we move the coop it moves with, the peat moss helps to keep it light. The container is about large enough for 2 standard chicken to bath together. I have 2 containers sitting in one other (stacked). They both have holes drilled in them for drainage, between the 2 container I have landscape fabrics(this prevents the "dirt" from falling out, but let's water drain).