Eat them! We love them boiled better than any other kind of egg (we eat chicken eggs occasionally but mostly duck eggs). They are sweet and perfectly balanced between yolk and white, and perfect bite sized. And yes, the children adore them. We're actually saving up to take several dozen to a family reunion for the Fourth of July.
We also scramble them and use them in recipes, but only when we're out of duck eggs. The duck eggs are firmer and richer and more satisfying, and also better for baking. But the quail eggs are just fine, and very sweet.
My husband sometimes fries one and serves it on a small piece of toast or a thick cracker (like a wassa or something), and it's quite delicious that way. But frying them is a lot of work for a single bite, lol.
You could also hatch them and sell the babies or eat their offspring... quail eggs are way easy to hatch...
Or you could leave them in a cool spot to dry, and then use them for decoration. They'd be adorable in little decorative nests and such, if you're crafty. If you leave an egg to dry out, after about a year it's completely empty and won't stink if it breaks (but don't break it before it's completely dry, lol!).
Or give them away. Or contact the local Asian restaurants and stores and see if they want to buy them for their customers. Or advertise them on craigslist for hatching or eating. Or feed them to your dogs or cats or ferrets. Or boil them, chop them, and put them in the quail food for extra protein.
Or ship them to me and I'll find a use!! LOL
But don't throw them away. They're too good for that!