There are special primers/sealants for plastic parts. They block the solvents in the top coat from reaching the plastic.
Also the top coat should adhere better when the primer was used.
Painting plastic is always a tricky thing. There are so many types of plastic out there and they all require different treatment.
Many plastic parts have a code somewhere on the back telling the type of plastic plastic, something like "PP", usually framed in a triangle.
You should go to an automotive paint shop and get the proper primer before you paint. They should sell it in a spray can.
On top of the primer/sealant you can probably use most common spray paints.
Might also want to ask a paint shop how much they want to paint the parts. It may not be as expensive as you think.
HTH
