For the unincorporated community, see Amenia (CDP), New York. Amenia is a town in Dutchess County, United States. New York, United States. The population was 4,436 at the 2010 census. The name is derived from the Latin word, amoena, which means "pleasant to the eye. " The Town of Amenia is on the east border of the county. The town has train service to New York City via the Metro North Railroad. The local train station is called Wassaic, after the hamlet of Wassaic--a part of Amenia.