How to cook a tender quail?
Three potential methods or changes you can try:


soak the quail in brine for 2-3 hours before searing. You can do this in a large zip-lock sack or in a covered bowl. Make sure to store the quail/brine combo in your refrigerator during the soaking.
Let quail reach room temperature before cooking.
Pan-searing the quail might dry out the smaller pieces, i.e. the bony wings or legs. Try your 20-minutes cooking in a very hot oven, making sure not to burn or sear the quail too much. Similar to cooking a turkey, cover the thinner pieces with foil so they dry out more slowly.


Ultimate method: use a "Sous Vide" method - you basically seal the quail and your flavorful broth in a vacuum seal bag, making sure to get as much air out as possible before sealing. Then you slow-cook the bag+contents in a Sous Vide hot-water bath. Instead of buying an expensive/French Sous Vide cooker, just follow these steps for very similar results: http://www.seriouseats.com/2010/04/cook-your-meat-in-a-beer-cooler-the-worlds-best-sous-vide-hack.html

Note: to get a good finish, after cooking the quail to tender in a Sous Vide bath, you can sear the quail a little bit with a cook's blow-torch (for good presentation) or just pan sear it quickly in a hot pan.