When working under the eyes, have your model look upwards - only with the eyes, without moving the head. If you work above the eyes (eyelid), have your model close his/her eyes in a relaxed manner. Children are inclined to shut their eyes tight. Then you can say: keep your eyes closed as if you are sleeping.
Hint: Regularly change the water you rinse your brushes in and preferably work with two water bowls: one for light and one for dark shades.
To make the eyes stand out more, you can draw black around them.