Palmyra is a town in Morgan Township, Harrison County, Indiana, United States. The population was 930 at the 2010 census. Palmyra was originally called Carthage, and under the latter name was laid out in 1836. Because there was already another Carthage in Indiana, the town was renamed Palmyra in 1839 to avoid repetition. The present name mos…Palmyra is a town in Morgan Township, Harrison County, Indiana, United States. The population was 930 at the 2010 census. Palmyra was originally called Carthage, and under the latter name was laid out in 1836. Because there was already another Carthage in Indiana, the town was renamed Palmyra in 1839 to avoid repetition. The present name most likely is a transfer from the ancient city of Palmyra.