What I do for eyes is first wash black/dark in the socket. This will show the lines better and make an eyeliner. Then I paint white ovals inside the 'eyeliner'. Then I paint the pupils black, but the pupils always have to go from top to bottom with no white on the top or bottom otherwise it doesn't look right to me.
I have tried making two white dots but it never looks right because the pupil never looks round. They look like cat eyes whenever I do it that way.
I've seen someone who got frustrated painting eyes that they just glued googley eyes on their troops.