Wash the peach stone, scrubbing it with a brush, until all the fruit is removed. Place the stone in a bowl and pour water over it. Allow it to soak for 24 hours.
Moisten a handful of peat moss. Wring it out until all the water drips from it, and it is barely moist. Push the peach stone into the moss, and place the bundle into a plastic sandwich bag. Seal the bag. Use a sharp instrument, such as an icepick, to poke three to five small holes in the bag for ventilation. Place the bag into the refrigerator, and allow it to remain there for 90 days.
Check the moisture content of the peat moss once a week. If it feels dry, sprinkle water over it until it is slightly moist, but not wet.
Prepare the planting spot by loosening the soil in a 1-foot-square area to 1 foot deep. Add a 3-inch layer of coarse sand, also called builders' sand, and 3 inches of compost to the soil. Use a shovel or garden fork to blend the amendments with the garden soil.
Plant the peach stone, wrapped in the peat moss, 1 1/2 inches deep. Water the area until the top 6 inches of soil are moist. Don't water again unless there is no rain for two weeks. The stone should sprout within one month.