Sand over the bad clearcoat lightly with a piece of sandpaper. For the paint to adhere to the clearcoat you must add a little texture with the sandpaper.
Fill a bucket with 1 gallon of water. Add 1 tsp. of trisodium phosphate (TSP) and mix thoroughly with a wooden spoon. Saturate a cloth in the mixture and wring out the excess liquid. Gently scrub the item with the cloth to remove surface dust, dirt and other debris. Allow the wood to dry before continuing.
Pour paint into a plastic paint tray. Saturate a clean paintbrush with the paint. Allow the excess paint to drip off the paintbrush into the paint tray.
Brush the paint onto the wood in short, even strokes. Apply the paint in the direction of the wood grain. Continue saturating the paintbrush with the paint and applying it to the wood until you have covered the bad clearcoat.
Allow to dry completely for 24 hours. If necessary, apply a second coat of paint until you achieve the desired look. Allow each coat of paint to dry before applying another coat.