Nearly all treatments that kill the lice/mites will need to be repeated in 7 days to kill what hatches from the eggs. I would personally use an insecticide like permethrin for the treatment. It's known to be safe and effective. If the infestation is bad, I would repeat treating the birds every 7 days for at least 3 rounds.
If they have mites, they can stay hidden in nooks and crannies in the coop as well as infesting the birds. That means that you would also need to completely clean out all bedding from the coop and double bag or burn it, spray down all surfaces in the coop paying particular attention to any place wood meets wood and re-bed. This cleaning would need to be repeated with each re-treatment of the birds.
Good luck.