The utilization of a low-frequency (<200 MHz) RF system in storage facilitates the attainment of ultra-low emittances in synchrotron light sources through on-axis injection. This paper focuses on the development of a low-frequency normal conducting (NC) cavity with higher-order mode (HOM) damping for fourth-generation synchrotron light sources. We propose a novel approach to achieve efficient HOM damping in a NC cavity by optimizing the lowest frequency HOM and implementing a beam-line absorber. Notably, unlike conventional NC cavities, the presence of a large beam tube for the beam-line absorber does not compromise the accelerating performance in a coaxial resonant cavity, enabling effective HOM damping while maintaining a high shunt impedance. Through simulations, the prototype design of a 166.6 MHz HOM-damped cavity demonstrates a fundamental mode impedance of ∼8 MΩ, with longitudinal and transverse HOM impedances below 2.0 and 50 kΩ/m, respectively.