I'll venture a couple of hints without having seen the cabinets. First of all you'll need to degrease them with a good washing. Even though they're in the pantry and not the kitchen you want to minimize surprises later. I'd also consider abrading the vinyl by running a fine sandpaper over it; The small scratches will give better adhesion while being invisible under the paint.
Primer is mandatory with a questionable surface. Primers have a higher concentration of resins, hence better adhesion than paints. I'd shy away from anything purporting to be paint+primer in one can though. Ditto for the "house brand" primers in hardware stores, get one you know will adhere to plastic.
If appearance is especially important your best bet is a paint store, which generally features better advice and products than hardware stores. Make sure you tell them you're painting over vinyl so you get the correct primer.
If cost is paramount, it's off to the hardware store. I know Rustoleum markets a bunch of specialty coverings, notably XIM high-adhesion primers. (Including a "bonder" intended for plastic.) I'd try a coat of that or the local equivalent under the paint of your choice.