The original factory installed engine was a Kohler K-341S. This engine produces 16 horsepower, and has a displacement of 35.89 cubic inches. It was an air-cooled four stroke unit, with a single cylinder. The shaft alignment was horizontal.
In 2011, Kohler manufactures the CH18 engine. This engine is slightly different than the original engine. First, it is a V-twin unit, meaning it has two cylinders in a "V" configuration. Second, it produces 18 horsepower, instead of the original 16. Its displacement is 39 cubic inches. It will adapt to the tractor, since the shaft is also horizontal. You may have to fabricate a new mounting plate, since the bolt hole configuration may be different.
The Kohler CH20 engine is very similar to the CH18, except it produces 20 horsepower instead of 18. You may want the extra 4 horsepower to power attached equipment, such as a garden tiller or to pull a small plow. Again, you may have to fabricate a new mounting plate, since the bolt configuration may not line up. Bear in mind since this engine is slightly larger than the original, you may encounter slight interference problems with other components when adapting it in.
The Kohler CH15 produces 15 horsepower and is the one most similar to the original K-341S. The engine has a 26 cubic inch displacement. It is a single cylinder unit, and shares many of the same size attributes as the original 16 horsepower engine. Because of this, it should fit with no interference problems.