I havent killed any of my chickies yet. But, if you have a Kerr canning book, or some other canning book it should tell you what to use in the stock. Personally I use stock for chicken noodle soup mostly but you could use it for chicken and dumplings also. Hmmmm, I am just guessing here but onions, celery, salt, pepper, maybe green peppers. WHat ever you like in your food as long as it is not noodles or beans or anything that swells up. You could look online also.
I canned some chicken down a little while ago. I cooked the chicken in the slow cooker and put water in to about 2 in from the top (I had 3 chickens in a 7 qt cooker). Then I added my seasonings and cooked overnight. The next morning I unplugged and uncovered so it would cool enough to handle. Then I loosely packed the chicken in the jars and used enough brooth to fill to 1/2 in from top of jar. The rest of the broth I canned separate. You can add vegs before canning if you like. Just remember if you can the meat it take a long time. Pints are 1 hour and 15 minutes and Quarts are 1 hour and 30 minutes. I don't recall the pressure but, I'm sure your book will tell you.