Actually the shoes aren't plastic, not the genuine ones. They are made out of Croslite. It is a closed celled proprietary resin. The shoes are designed not to have anything stick to them. I'm not sure what kinds of paints would work. Crocs are non-porous. The paint won't soak into the shoes. Also, because of their flexible nature, I would think it would be hard to find a paint that can withhold bending all of the time.
Some people decorate crocs other ways. There is a company who sews theirs. it's at http://roscom.co.il/
But with adding any material to crocs other than croslite, you are compromising its benefits. Crocs are anti-microbial, meaning they resist bacteria. If you ad string to them, they are no longer anti-microbial.
Crocs are cool though. I give you props for trying to make them your own.