The GAPS-diet folks say that shorter cooking times when making bone broth result in more gelatin, and I've noticed that my bone broth gels up more consistently when I do a short cooking time, say 4-6 hours. Since I love chicken broth, I'd probably put a chicken carcass in a slow cooker and then add flavors I like to make a tasty light soup--for me, a bit of sauteed onion and garlic, a few herbs, and just drink it with meals.
We also have bernard jensen's powdered beef gelatin and that would thicken sauces. In a pinch, you could just dissolve it in warm water and drink it plain with a meal--not very tasty, but not bad or offensive.