@TeraLa
It's difficult and complicated to change a tourist visa into a business visa - not impossible - just difficult, complicated, and you'll have to pay a penalty/fee for the conversion.
It's NOT difficult to extend your tourist visa - just visit the Visa Office (also called Entry/Exit office) in any city, to request a tourist visa extension - they'll usually extend for 2 weeks to up to 3 months (maximum).
Converting a tourist visa into a business visa requires an employer/employment letter and a host of other documents that would need to be authenticated (notarized and then authenticated by city, state, and national government agencies), to include your college diploma, criminal background check, and a health check for communicable diseases (STDs) and general health.
If you want to stay and work in Kunming - you can check out various English language (or other language) schools - but you'll still be required to provide the above documentation before you're allowed to work here. You MIGHT be able to exit into an adjacent country (Thailand, Malaysia, Vietnam, Burma, Laos, Cambodia, and maybe even Hong Kong), while you're collecting the documents, but you absolutely cannot work legally without those docs.
An alternative - if you're trying to buy/sell products/services in China for a foreign or offshore company - you can explore the Representative Office path - but you'll have to pay to be seconded under your own or an existing representative office - all the usual visa fees plus the rep office administrative fee.
If that's your path - then contact <longdragon> on this website.
Once you're seconded under the rep office and you have your work visa documents in order, you can look for gainful employment (if you qualify) - but you'll need to convert and transfer your visa to the new company (which they'll pay for).
The government will issue you a temporary work visa - and once you're in-country - you'll need to apply to convert the temporary work visa into the semi-permanent work visa (typically year to year for newbies).
Hope that's helpful.