Waverly is a city in Coffey County, Kansas, United States. As of the 2020 census, the population of the city was 574. Waverly was founded in 1…Waverly is a city in Coffey County, Kansas, United States. As of the 2020 census, the population of the city was 574. Waverly was founded in 1878. It was named by a pioneer settler for his hometown of Waverly, Indiana.