I use a .35Whelen, a .350Rem Mag, 45-70, or a .338Win Mag. Not for the Black Bears I kill, but for the Grizzlies that sneak in and leave us no other option.
black Bears are easy to kill, just like said earlier. 1/3rd of the way up on the shoulder. Use a good penetrating bullet like the Nosler Partition.
ChrisK: Want to make life a real adrenaline rush. Save up your money and come to Alaska. My hunting partner will only hunt bears with me if he can be 15ft up in a tree stand when I start calling. I purchased the Wood Wise, Black Bear Talking call. It comes with a warning "Do Not Use If There Is A Possibility A Grizzly Might Answer The Call". It's a rush when a Grizzly comes in with a big rush ready to kill something. Grizzlies kill any Black Bears they find in their territory. You do not want to be on the ground when a Grizzly comes tearing into your area. I've had guys scream when the Griz hits their tree. the Griz comes in so fast and with so much power, it's frightening to some people. Makes my heart pound, and I've done it more than a few times.