Center Conway is an unincorporated community within the town of Conway in Carroll County, New Hampshire, United States. From the late 19th century until the Second World War, Center Conway was known for its corn cannery. Today the homes are mostly residential, with many vacationers visiting the scenic Conway Lake. The old corn farms hav…Center Conway is an unincorporated community within the town of Conway in Carroll County, New Hampshire, United States. From the late 19th century until the Second World War, Center Conway was known for its corn cannery. Today the homes are mostly residential, with many vacationers visiting the scenic Conway Lake. The old corn farms have given way to modern businesses, though summer corn is still harvested from local corn fields.