native literature, local literature or country literature?

I'd go with country literature. In many contexts, "native" means to an English speaker the cultural artifacts of an aboriginal people as opposed to the cultural artifacts of European invaders and colonizers. Of course, native simply means born in the land to which one refers, but it is often used in English to denote aboriginal inhabitants as opposed to inhabitants descended from colonists.

Local literature could be said of an urban writer as well as of someone from the countryside, or someone writing about the countryside or the city, so that would not convey the sense you want. "Local-colored" literature does not sound like something a native speaker would say, although there is nothing "wrong" about it--it's just awkward.

I might go with something like "literature of rural life", "literature of life in the country", "stories of traditional Chinese life", "stories of modern Chinese life in the country", etc. (depending of course on which it is he's writing about), rather than an adjective before the noun.

I agree with you. As a matter of fact, "country literature" is my translation, which is an "immitation" of American "country songs."