Yes. A wonderful product called Seapaints will work great. No prep needed. Just make sure they are clean and wipe down with alcohol. Paint and then use their poly. www.seapaints.com
Paul: I've painted mine! Wash well, PRIME! and use two coats of a GOOD latex paint. I'll attach a photo of my little kitchen.... I did add new hardware --- as painting over hinges is no bueno.
Prep is the key to any successful paint job I've ever done. I start with a completely clean surface. TSP or a TSP substitute like Krud Kutter. After clean and dry, dull the finish by sanding. You are removing any gloss or surface finish. Wipe it down carefully with a tack cloth or damp microfiber cloth. Use a good sealer to give your paint a good surface it can attach to. I wait overnight, even though you could probably paint sooner, depending on the product you use. Once it is dry, I look at it carefully, to make sure I didn't miss any spots and that the sealer is adhering to the old finish. It's easier to fix anything at that point. Then once I am sure it is good to go, I use a good quality paint. A clear, water based sealer, won't yellow once your paint is on and dry.. Tape anything you don't want paint on. Remove hardware and doors if possible. Label them so you know where to reattach them. I have painted doors without removing them, but it is harder to avoid drips and to get a smooth finish. Hope this helped.