I own a Wright Sentar mower with a Kohler CV23S engine that has 840 run hours on it. Three weeks ago it was running fine, suddenly the engine RPM dropped, and it began to backfire, blowing black smoke out of the muffler. I installed a new gas filter and spark plugs. Both cylinders show a strong spark and seem to be getting gas but only the one by the fuel pump seems to have any power. The other cylinder backfires with every spark, blowing black smoke out of the muffler. I need help determining what the problem is. Has anyone had a similar problem, and how did you fix it?
Thanks.

How does the spark plug look on the "bad" cylinder, black and sooty?
 
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I changed oil, filters, and plugs earlier this spring just before the problems started so the plugs on both cylinders have little run time on them and both look pretty clean.

Black smoke is excess fuel going thru that cylinder. Low compression
in that cylinder would hamper combustion. 
 
You may want to check valve clearances..
 
You need to check compression on both cylinders but even better
a "Leak Down" test.  
 
This will determine the health of the engine, rings, valves and more
importantly, the HEAD GASKET (may be blown)..
 
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