Dielectric elastomers (DE) are incompressible rubberlike solids whose electrical and structural responses are highly nonlinear and strongly coupled. Thanks to their coupled electromechanical response, intrinsic lightness, easy manufacturability, and low-cost, DEs are perfectly suited for the development of novel solid-state polymeric energy conversion units with capacitive nature and high-voltage operation, which are more resilient, lightweight, integrated, economic, and disposable than traditional generators based on conventional electromagnetic technology. Inflated circular diaphragm dielectric elastomer generators (ICD-DEG) are a special embodiment of polymeric transducer that can be used to convert pneumatic energy into usable electricity. Potential application of ICD-DEG is as power take-off system for wave energy converters (WEC) based on the oscillating water column (OWC) principle. This paper presents a reduced, yet accurate, dynamic model for ICD-DEG that features one kinematic degree of freedom and which accounts for DE visco-elasticity. The model is computationally simple and can be easily integrated into existing wave-to-wire models of OWCs to be used for fast analysis and real-time applications. For demonstration purposes, integration of the considered ICD-DEG model with a lumped-parameter hydrodynamic model of a realistic OWC is also presented along with a simulation case study.