Human, I agree with you about the binary of capitalism and communism, but to give the OP credit, what is a non-statist, non-hierarchal, and non-capitalist set of social relations if not communism? Ingrate, I understand where you are coming from, but some pre-capitalist societies had hierarchies, which anarchists would disdain. As for the ones that didn't, they might not have been big "C" communist societies, but they they certainly were "communistic."
I'm not sure it's a given that "communism" describes a non-statist or non-hierarchical set of social relations. It certainly may, but I there are far too many ways for the "common" to be elevated into a position above the constituent individuals. I guess everything depends on how you're defining your terms. Either "capitalism" refers to a specific system that involves systematic exploitation, with can be differentiated from other systems that involve trade, in which case there seem to be any number of possible alternatives, or else "capitalism" refers to everything that is, well, not "communism," and the question is answered in the asking. Anarchists started with an analysis of capitalism ("property is theft" and all that) that doesn't beg the question, while the introduction of marxist economics seems to drive the other analysis. So, I would be inclined to point to "mutualism," "collectivism" and the like as examples of non-capitalist and non-communist arrangements, provided the definitions leave the question open to answers.