Looks like the .308 Win has overwhelming support as a black bear snuffer. As I recall, my first 3 bears were all shot with a Rem Model 7 in .308 shooting 165 grain Partitions. They all died where they were supposed to -- within a few feet of where they were shot.
The one thing I'd recommend for black bear, regardless of the cartridge used, is to make sure the bullet you're planning to use can be counted on to exit the animal regardless of shooting angle. Now don't get me wrong -- you want decent expansion from that bullet as well. But if Yogi decides to take a bit of a tour before expiring, you absolutely want an exit wound in order to facilitate some kind of a blood trail. It's nothing short of remarkable how much blood their hide and hair can soak up -- and if you only have one hole on the way in and nothing on the way out, you typically won't have much to follow.
Incidentally, should it ever happen that you have to follow a bear without much sign, do your best to remember the bear's last known direction of travel. In my experience, they will tend not to deviate from that path very much. And go slowly -- on a couple of occassions I've gone on merry marches after one, only to regroup at the initial crime scene and discover that I had walked right past an expired animal that within 50 yards had dived under a brush pile and simply disappeared.