Did you clean and sand thoroughly first? Then clean, then prime, then paint? We've painted over these types of cab's for some folks in the past and if prep'd right, they come out ok.
You need "laminate paint". First you need to prime them with laminate primer...
There's a product by "white knight" that is specifically for this job. I've used it and it's fabulous! Also look at the range "rustoleum" have. They cover a wide variety of diy with their paints... They actually have a spray called "2X" which bonds to wood, plastic, vinyl, iron, metal, pretty much anything. I work in paint everyday and sell these products here in Australia. Hope that helps:)
Remove all of the doors and scrub them thoroughly using TSP (ask at the hardware store). Then buff really well with fine steel wool and wash again. Make sure they're completely dry and spray them with a paint that can bond to plastic. @Tanya McIntyre mentions some good ones. It's all in the prep work. Good luck!
A friend painted my mobile home kitchen cabinets white (they were yukky oak 1959 paneling). He washed them then used primer plus paint. That was five years ago and they still look good.