Home Postcode finder TAS Black River Black River postcode TAS Black River is a locality in Tasmania covered by postcode 7321. Postcode 7321 State or territory Tasmania (TAS) Region Tasmania Add a free Black River business listing Be the first listing in Black River Common questionsWhat is the postcode for Black River?Black River, TAS has the postcode 7321.What state is Black River in?Black River is in Tasmania (TAS).Does postcode 7321 cover more than one suburb?Yes. Postcode 7321 covers 35 localities, so the postcode alone does not identify Black River. Browse other postcodes in Tasmania, or widen the search to every Australian postcode.