It can be done, but you need to be pretty good at painting, so practice on some old doors first.
In warm, dry conditions, you can paint plastic with a single flowing coat of oil-based non-drip gloss, using a soft bristle brush that has previously been well-used and thoroughly cleaned (this soften the tips of the bristles and sheds any loose ones). About a 2-inch brush will probably suit you. You can use a half-inch sash brush as well if it has mouldings. Do the mouldings first, then the panels, then the uprights and stiles, then don't touch it until fully hard. This method does not need a primer or undercoat.
you must clean the plastic thoroughly first, including dtop, bottom, edges and crevices. Firstly with a stiff brush, detergent and hot water; finally with a green pan-scourer and white spirit, which will remove any grease or black mould or eroded plastic surface. Then wipe clean.
You can practice by painting plastic pipes, meter boxes etc.
Paint after the sun has shone on it and has then moved away so the article is now not in direct sunlight.