Someone more mechanically-minded might be able to suggest exactly what you're after but last year I used animated eyes from an iPad app to give a photo "crazy eyes". It was surprisingly effective.
Came here to say this!!!if you are looking for easy peazy no big dealzy, check out the "digital duds" app for your cel phone. There are multiple different effects, and you may be able to make a duct tape pocket on the back of the picture, cut out eye holes and viola, moving eyes in the picture.