Cultured marble countertops do contain marble dust, but they're not natural stone; they're actually closer to fiberglass or resin -- which means that, if the surface is discolored, scratched, or you're just sick of it, you can paint over it in good conscience. The challenge is getting paint to stick to the slick surface and stay there through future use. One trick is to use floor-grade paint and polyurethane, which are made to stand up to foot traffic and so are tougher. Use oil-based applications, which dry harder than water-based.
Remove any fixtures that are attached to the cultured marble, including handles, soap dishes or faucets. If the countertop is caulked at the wall, use your razor knife to cut out the caulk.
Load your orbital sander with 150-grit sandpaper. Sand the surface in sections, moving the sander slowly back and forth. Hold the sander firmly enough that it takes the shine off the countertop, but don't use so much force that you gouge the surface. Continue until the surface looks dull from all angles, with no gloss shine left. Thoroughly wipe it down with a damp sponge to clean up the dust, then follow up with a dry towel.
Put painter's tape and newspaper all around the edges of the countertop, covering all parts that won't be painted. Spray a very light, even coat of sealing primer on the whole surface. Let it dry for two hours, then spray a second light, even coat, so it's completely covered.
Apply your top coat of paint in the same manner, spraying it very lightly and evenly in multiple coats, to prevent drips or streaking. Let it dry for two hours between coats. Lay at least three coats, then judge from the look of the surface whether it needs a fourth.
Open your polyurethane gloss and gently stir it (don't shake it, as that will cause bubbles). Gently brush a first layer over the surface, in slow, careful strokes. Avoid forming bubbles. Let it dry overnight, then very lightly hand-buff it with 220-grit sandpaper, just enough to dull the shine. Lay a second coat, let it dry, buff it, and lay a third coat. Allow the third coat to dry for two days before using the countertop.