Painting over finished wood is always risky, which is why pros recommend stripping and sanding off the old finish. That isn't always practical or feasible, though, and it is possible to paint over polyurethane and get good results. The risk of peeling will remain, however, unless you properly prepare the finish by scuffing or removing the gloss and applying a high-quality primer prior to painting.
Risks of Painting Finished Wood
A film finish like polyurethane is designed to be hard and impermeable to liquids, which are two qualities that act against paint adhesion. Polyurethane prevents paint from bonding directly with the wood, and because it's a plastic, paint can't bond to it in the same way.
Without proper preparation, a polyurethane finished cabinet is already a poor candidate for painting, but it's even more so in the kitchen, where it has probably become enveloped in a thin layer of cooking grease and oil. Paint will bubble, peel and crack, sometimes even before it dries, because it simply doesn't stick. Even if it does stick, the polyurethane undercoat may have already started cracking and lifting with age.
A Three-Step Preparation Routine
To successfully paint over polyurethane, you need to do three things, as described by the Handyman's Daughter. The first is to clean the surfaces you want to paint. Mix a strong detergent with warm water and scrub all the surfaces thoroughly. Trisodium phosphate (TSP) or a TSP substitute are recommended, because they dissolve oils and greases that may have become hardened. Mix 1 cup of TSP per gallon of water. Wear rubber gloves and goggles while cleaning to protect yourself from the caustic cleaner.
The second step is to cut the polyurethane gloss, which you can do in one of two ways. You can sand the finish lightly with a pad sander and 150-grit paper. Remember, your goal is to scuff up the finish not wear through it, so use light pressure. The alternative is to wipe or brush on a chemical gloss remover according to the instructions that come with the product you purchase.
The final step is to apply a primer, such as Kilz stain-blocking water-based primer or a similar product. Applying Kilz over polyurethane serves two purposes. It adheres better to the scuffed-up surface than paint, and it provides a white undercoat, which saves paint if you are using a light or pastel paint color. As a bonus, it prevents any dyes or stains that you weren't able to clean off from bleeding through.
Painting Is the Easy Part
Once you've completed the prep work, you should be able to finish the job by applying two coats of water- or solvent-based enamel, either by spraying or using a brush. A handheld airless sprayer is an inexpensive tool, and it gives better results than brushing. However, using an airless sprayer requires even more preparation, because you have to mask off areas that don't get painted with masking tape and paper. You should be able to skip most of this extra prep work if you use a paintbrush and you're reasonably careful with it.
When brushing cabinets, you'll get top results if you avoid streaks and crisscross stroke patterns by always stroking with the grain of the wood. When you have to brush cross grain to get into crevices or corners, give a final finish stroke that goes with the grain.