There are a couple ways you can attach the spoon eye to the face. First you can just glue it to the face with something like hot glue or other adhesive.  Second you could drill two tiny holes at the top and bottom or in the corners of the eyes and sew it on through the holes. The second option works best if you are planing on covering the eye with fabric to make an eyelid. 

I was thinking glue would be tough because of the concave of the side you are attaching to the face.  As for the sewing if you are only sewing the top where they eyelid would cover would that make it so the eye would not be securely attached and perhaps move around?

Well an eyelid normally comes to the corner of the eyes. So you have three points where you drill holes top and then two sides.  Should hole securely.  You are right that with the concave you only have surface at the edges to glue. You could try to fill in the concave with something like maybe foam that is glued to the spoon and then glue the foam to the face.

The best luck I've had personally with glue and spoons is crazy glue. It's clear, it has a tiny point of exit on the bottle, and you can get a superthin line on the edge of the spoon. Drawback is you really get 1 shot at it.. So mark your spots so you line it up right the first time! The crazy glue tears up the fabric coming off to "re-try" or you can exacto under it and hope for the best...

Thanks I'll keep this in mind.