What type of paint for mildly flexible plastics?
Elastomeric paint
 And the asnwer you are looking for...
 Acrylic Paint 
Acrylic paint is indeed very elastic, as the comment section points out: It prevents cracking from occurring.

Other Options
There arent really 'other options that doesn't contain acrylic based paints... one of them is called: Urethane, this bad boy is basically modified acrylic paint.
Elastomeric paint Would be your final answer