Step 1- gently rub the current deposits off with a damp cloth that is non-abrasive
Step 2- place pebbles in vinegar for half an hour (30 minutes), apply some baking soda, creating a paste. With the non abrasive cloth or sponge, firmly rub the pebbles for a while to remove the stains.
Step 3- rinse and then rinse again. Make sure all the baking soda and vinegar are off.
Step 4- dry with a non abrasive cloth to get the water off.
Step 5- place pebbles back in the fountain.
The above should work if you are dealing with hard water staining and not something else which may be in the water.