Spray paint manufacturers have developed single and multi-step products that mimic stone. Application consists mainly of prepping the surface by cleaning and roughening it for a better bond, then using a spray can or two. Some products have a material that's sprinkled onto the wet paint to give it a more realistic texture. A mix-and-match approach can also be employed to alter the stock colors. Although standard outlet covers can be used, metal will be more durable.
Creating a truly realistic-looking stone-like surface with paint is an in-demand skill. Among the more popular techniques employed by practitioners of the art is the use of multiple layers applied with brushes, sponges and other inventive applicators such as feathers. The idea is to create the subtle color variations seen in nature, as well as random mottling and veining. It takes practice, and each completed piece is a work of art. If you go this route, be prepared to spend a lot of time at it, since faux painting can be a detailed endeavor.
Craft supply stores sell molds for making outlet covers out of epoxy resin. Depending on the effect you hope to achieve, casting resin can be mixed with real stone chips and dust, different colorants, or both. Polyurethanes and other kinds of plastic casting compounds provide another option.
If you want outlet covers that are an exact match to a newly manufactured stone countertop, contact the company that made or installed the counters. Many now offer matching outlet covers separately or as part of an installation package.