We all know at least one person who seems to have his/her eyes closed in every picture. They don't do it on purpose, and when they consciously try to keep their eyes open, they end up looking like a deer in the headlights. This is a simple solution that has worked for me 99% of the time.
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Have the subject of your photo close her eyes. Instruct her to open her eyes on the count of three. Start counting, and as soon as she opens her eyes, snap the photo. It may take a few tries to get the timing down, but the end result is a picture with naturally open eyes. Often times, you'll get a real smile in the process because the whole thing is a little goofy.
Give it a try next time you're shooting that person. Let me know in the comments how it worked for you, or if you've found another method that works better for you.