I've shot a lot of black bears with calibers like 7mm's, and even 25's.
In the 7mm, 140 grain or 160 grain TSX's would be my bullets of choice.
The only reason I'd prefer a bigger calibers (as black bear guide JJHack - see the ad at the bottom of the page - has written many times) is that fat fall bears have a lot of fat that sort of seals the wounds and hair that absorbs a lot of blood. Couple that with the fact that many prefer really dense habitat, that they are often most active just before dark - and the fact that they have no hooves to dig into the ground - combine all that and you realize that you have one of the hardest animals in the world to track - if you don't drop it near where you hit it.
So, a bigger caliber is always better - if you have access to one.
It's not that they are difficult to kill - only that they can be tough to track, with the thick habitat, lack of hooves and lack of visible blood - especially near dark.
So - with a 7mm08, stick to a real "penetrating" bullet, pick a shot that lets you shoot through both shoulders, and don't shoot in really thick stuff - at least if it's close to dark.
Other than those few shortcomings, 7mm-08's are fine black bear guns - with good bullets - and remembering these simple facts.
This one was killed (in really thick stuff) with a 25-06,the last shot was at about three yards (you can see the killing shot in the head) - in the total dark, with a flashlight in hand, (after I finally located it) - after tracking it, and after wounding it late in the evening. Talk about adrenaline! This picture was taken the next morning.
This brown was shot with a 7mm.
And this little *%#$ - (who actually came at me!) - out of one of my fruit trees - from less than ten yards away - with a 7mm-08. Out of the 360 degrees he could have ran - he had to come for me to proove how tough he was - so he ended up dying. Two year old, human-habituated, males, can be trouble!