Craftsman LTS 1500 lawn tractor won't start

My push mower engine is running roughly -- it has extreme vibration, it sputters like it is about to die, and black smoke comes out of the muffler. The mower is a Craftsman 21" with a B&S 6.0hp, model 122K02-0577-E1, and is 2.5 years old. The fuel line is not clogged, and the carburetor seems to be in good condition with no obstructions. I do not think the gas is bad, because it has been used in a neighbor's mower with no problems. Just in case, I put some Stabil in the tank, but it did not help. I also changed to spark plug to no effect. Thanks in advance for any suggestions.

I think my JD 155 lawn tractor is overheating. After running about 1/2 hour is simply dies. It will then backfire on attempted starting. After cooling, no problem starting - but cycle repeats. Today's weather: 90+F, Midwest humidity. I have already removed the engine (Kohler CV15S - 15 HP) cowel and cleaned out the mouse debris. (Ongoing problem.) No problems with the Big Three (fuel, air, spark). Any advice would be appreciated.