How can I get a visa that is valid for more than 4 months?

A single-entry visa is usually valid for 3 months. If you want a visa valid for more than 4 months, you may apply for a double-entry one, which is usually valid for 6 months. However, a double-entry visa is more expensive than a single-entry one.
Another way to figure it out is to apply in a thrid country when you are traveling there. But not all China embassies or consulates issue visas to tourists from a third country.