For painting items such as accessories, being shoes, earrings, bracelets etc which are made of hard plastic, use the type of acrylic paint that is used for toy model cars as this is somewhat different to goauche. This paint can be purchased from Hobby stores, the type that sell paints for model cars.
The difference between the two paints is that gouache paint dries much faster and is best for the doll’s faces and works best with the vinyl faces. If you use the model car type acrylic on the face, each coat takes a long time to dry. But with hard plastic, the gouache tends to peel off, even after sealing it, it can peel. So the model car type is best for hard plastic for items such as shoes and earrings, as it will last better on that type of plastic. But if you were to paint a small section that is unlikely to get touched, the gouache can be okay. It’s just that the other type is slightly better.
With gouache paint on the doll’s vinyl faces, it stays on them very securely once it is sealed, even if you need to wash the doll, the face paint will stay secure, as it works well with the vinyl. So these are the two different types of paint required for these two types of materials.
One mention about enamel paint on hard plastic, it can work, but it takes a very long time to dry and you can end up with a layer of dust by the time it’s dry which isn’t a nice look. So I do recommend using acrylic over enamel for hard plastic objects and sealing the paint once the coats are complete.
Now for a tutorial on repainting dolls. This tutorial has the steps with photos to explain the process.