We just mulched a large part of the yard with locally sourced finer wood mulch, and we are going to build a larger run surrounding the coop on that. If it gets too yucky or isn't working we are building in 6" boards around the edges so we can use sand instead. Right now they free range in the yard and have unfettered access to my garden and our grassy area.
Their coop is under a big shady tree and their run will be a good spot to contain them during the heat of the day and when we don't want them free ranging. They have the gambrel style pre-fab coop that I don't love(it works for us in the burbs right now, we are buying a home with more space in the next 12-18 mos and will build a bigger one from scratch then) but it does have a small sand run under the main coop that they use for dust baths.