A masonry stain might work. A masonry stain will give you a more natural look without looking painted. This idea depends on the type of stone and its porosity.
If possible, try to identify the stone type and find some available for purchase. You will only need one or two pieces. Call your local paint stores and find out which ones carry masonry stains. Take the stone pieces to your local paint store and have the sales clerk apply a little to the stones to see its affect.
If the stone will accept the stain then your in business. Now you will need to choose a color.