BooGinHead Sippigrips. They cost less than $6 at a local baby store. (Our girls wwouldn't take them, but you can buy matching pacistraps too.)
This is a product that I give a thousand thumbs up. If you sew you could probably make a similar product very easily. It's simply a strap, one end straps with velcro to the high chair, stroller, car seat or whatever, and the other straps around the cup itself. (It has a grippy material on the back side which helps it to hold to the cup.)
I now own three of them. I keep one in the diaper bag, one on the high chair and one in a drawer for when I'm washing one of the others.
Great product and totally worth the price!