silver cleaner will remove the stains you can buy it at any supermarket or wilkinsons..or jewellry shops..soak the rings in some neat washing up liquid and that will start to lift the stain..
Hi missmooncat, I've done this loads of times (but with earrings not rings) everytime its happened to me, I have found that after a few days, my earrings have been back to normal (probably shampoo is cleaning them)