Post #13 ^ except: first get the unit in a well-ventilated place near the laundry area so the new paint won't get scratched moving it through several doors. At Lowes/HomeDepot/OSH you can find the epoxy appliance spray cans. (About$5) Buy ONE, take it home, spray an inconspicuous spot on the WASHER, let it dry, and compare the new color/texture to the factory white. If it matches enough to suit you, then pick up two more cans, a cheap plastic drop cloth, a roll of blue masking tape and a quart of odorless mineral spirits or whatever solvent they recommend for "wax and grease remover." Using clean non-linty rags and rubber gloves, wet one in remover, rub down one side, then wipe very thoroughly with the dry rag. Proceed the same way with the other sides. Make sure all the solvent is evaporated, then mask off all trim and stuff you don't want flecks of paint on. Spray the first coat very lightly, you'll just be putting a uniform layer of paint flecks on, not a smooth coat. Let this harden a few minutes, then put on another slightly thicker coat, but the beige will probably still show through. Let it harden a few minutes, then more thin coats until all the beige disappears. Let dry, inspect under good light and touch up areas where the color/sheen is not right. Wait two hours, pull off masking, carefully put it in place.
Notice I didn't say to sand before painting, a good practice but not necessary in my experience with epoxy appliance paint. I painted a refrigerator in a rental unit a while back and the paint is still good. Easy to touch up, just clean well and re-spray the affected area. On another refer, a scratch touchup lasted ten years.
Epoxy stinks like hell and will make you sick, so either get a $35 respirator at paint store or set up an exhaust fan nearby and paint downwind.