Black bears can be as large as grizzlies with the record black bear nearly 900 pounds in the wild. Many areas harvest black bears over 500 pounds each year. Certainly, the average black bears are going to be in the 200-300 pound range, but in my opinion, you should prepare not only for the average, but the outside range bears as well.
In that case, the weapon you consider adequate for a grizzly should be the consideration for a black bear as well since their size can overlap. For myself, that is a .44 magnum which many consider too small, but it does have the power and penetration with proper shot placement to do the job.
Secondly, the most likely bear attack will be a predatory male black bear according to the most recent research. Yes, most black bears will run when they encounter people, but once again, you are not preparing bear defense against a bear that will run away, you are asking that question for the bears that DON'T run away. A sling shot is enough for a bear that will run away anyway.
Bear spray does not work as well with black bears as it does with grizzly according to the bear researchers. Black bears have a tendency to come back after being sprayed once, twice, three times or more waiting for their opportunity if they are in a predatory mode. In that case, yes, the bear spray might buy you time, but since you can't climb a tree against a black bear to get away, you either have to be close enough to shelter or a car to escape or take care of the situation yourself. In that case, an adequate caliber gun is your best option.
Lastly, if you are hunting coyotes, consider a varmint gun that will do in a black bear as well. That would likely be .270 or .308 level rifles at a minimum. Little bit big for a coyote, but since the issue is hunting coyotes in bear country, a rifle is going to get you more power than almost all handguns. Consider your primary weapon your rifle with a good back up gun and don't forget not to hunt alone. Having another person to save your hide in the event that all of your other preparations fail is the most prudent way to go about the issue.
