I would think about trying Krylon Fusion spray paint. If the corners are in good condition and no gaps exist, it should bond to the vinyl surface (if that's what the boxes have) and give any other coats something to hold onto. I believe they make a compatible primer, too.
Another possible choice is using a vinyl dye, assuming the cabinets have vinyl surfaces. Then, a compatible paint can be used- this needs attention because some paints will dissolve the previous coat.