Coburg is a city in Montgomery County, Iowa, United States. The population was 26 at the 2020 census. Coburg got its start following …Coburg is a city in Montgomery County, Iowa, United States. The population was 26 at the 2020 census. Coburg got its start following construction of the railroad through the territory. According to the United States Census Bureau, the city has a total area of 0.29 square miles, all land.