I've always found that for animation, you can find all sorts of sizes of glass beads at Hobbycraft.
If you're doing a close up shot of the characters eyes and you don't want the holes to be visible, cover over the paint area with some black plasticine (for example). However, when animating the eyes, you'll have to keep taking off and re-applying the plasticine on the eyes after each movement.
If you're using a complex armature, you can fix magnets to the head of the armature and then use metal balls (sprayed to colour of your choice) which will stick to the eye sockets without need for clay, glue etc. However, you will need to drill holes in the metal ball bearings to be able to move them.
Hope this helps.