I have only tried to clean stones that I have reset to remove most of any dirt that may have accumulated from the soil it had lain on and that only, as said by Stephanie, with plain water and a natural or nylon brush. An interesting observation I have made on several stones is that the side of the stone which has lain on the ground has only dirt residue easily washed off while the side that was face up usually can't be cleaned due to the polluted rainfall. I would say any privately owned cemetery that needs care would have to provide the caregiver written assurance that the caregiver would not be liable for any non-malicious damage. Further, I would not use ANY solution to clean a stone except tap water. The risk is just not worth having a "clean" stone.