If the owl won't be played w/ by a small child. You could just use a hot glue gun to 'glue' the eyes together. You could use buttons (that way you can place them on top of each other exactly as you want) or just use felt for the eyes. You can control the eye shape better that way.
Hot glue works great gluing things together- but, wouldn't be a good choice for a small child's toy.
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