there are several products you can use but you have to be careful that those products do not harm the surrounding vegetation. I would suggest you first wet the stone with clean water. Next mix a solution of a  good neutral cleaner and spray it on the stone. Scrub with a soft bristtle brush. If this doesn't remove the stains than take and mix a solution of sulfamic acid and spray on the headstone. Agitate and than rinse with plenty of water.