What kind of paint best adheres to doll/barbie bodies?
Plastics have become less adaptable to paint and vinyl plastics are often the least receptive.  However, I think if you went to a distributor like Blick and visited the sign painter's paints, "One Shot" being the most prominent, you will find a very palatable product. 

Palatable in the sense that they mix well, so you can buy a few small jars and blend a skin tone.  And palatable because they just are the best enamel paints ever developed for commercial use.  They are heavily pigmented so they can be reduced and sprayed.  They lay down well and don't leave heavy ridge lines when strokes over lap, should you chose to paint with a brush.  They dry quickly and provide an even gloss finish, which can be flattened if desired.