Remove all the old paint located on the compound bow with mineral spirits. Pour a small amount of mineral spirits on a clean cloth and wipe down the bow to loosen all of the paint that still remains. Run the cloth over the entire surface and add more mineral spirits, if necessary.
Scrape off the excess paint with a paint scraper. Press the scraper firmly against the bow and run it along the bow until all of the paint is removed. Pick up any loose pieces that are laying around.
Pour dish soap on a clean rag and wipe down the surface of the bow to remove the remaining mineral spirits and other grease that still remains. Dampen the rag and scrub thoroughly until the surface is clean. Dry the area with a rag.
Lay the bow down on a flat surface directly on top of a tarp. Pick the desired color spray paint and hold it about four inches from the surface of the compound bow. Spray the bow beginning at one end and working toward the other. Move the can back and forth over the entire surface until it is completely covered. Let it dry for one hour.
Flip the bow over and repeat the same process for the sides and the bottom. Let them dry thoroughly and add a second coat, if necessary, to achieve the desired color. Inspect the compound bow and verify it your desired color and that you did not miss any spots.