Chicken sticks to bottom of pan when I boil bones for soup
Don't boil it.

You want a bare simmer when trying to extract the flavor from the bones.  If you're boiling, you'll both run into the problems that you mention (sticking &amp; burning), and you end up with a worse broth -- much of the flavor is in the smell of the soup, and boiling too hard will both destroy compounds you want and kick them into the air (and thus not in the broth/stock).

My normal procedure is:


With either a good cleaver, or poultry shears,can crack the longer leg and thigh bones.
Cover with cold water by an inch or so.
Add whatever scrap vegetables you have.  (whatever you have that's getting a bit sad looking in the fridge, but isn't to the point of being spoiled.  I also have a bag in my freezer of vegetables that were past their prime).
Heat the water 'til you see bubbling, then back off the heat to maintain a bare simmer.
Cook for 2 to 4 hours, checking on it every 30 min or so.  (Once you're more experienced, you may not need to check on it as often ... but you need to watch for the water evaporating too quickly or things starting to stick)
Strain out the bones &amp; vegetables.
Cool down the broth if not serving that day, put into smaller containers, and put in the refrigerator.
On the day you're serving it, add in whatever diced vegetables and/or meat and heat through.  Adjust the salt &amp; acidity if needed, and maybe add some herbs.
For something starchy like stuffing, heat it through separately and put a scoop in the bottom of the bowl, then pour the hot soup over it.  (to avoid it turning into complete mush)