This paper presents a novel design method for high-frequency dielectric elastomer actuator (DEA) applications. A DEA consist of a mechanically pre-stretched elastomer film sandwiched between two compliant electrodes, which expands when subject to a high voltage. While the design of low-frequency DEA applications is generally well understood, up to now there is still a lack of systematic design rules for DEA systems operating in dynamic applications (e.g. pumps, compressors, and acoustics). The goal of this paper is the development of a novel graphical design approach which permits to systematically address the design of high-frequency DEA systems. A pneumatic diaphragm pump driven by a cone DEA is considered as a case study for validation of the new design technique. By means of the proposed method, the actuator performance can be quantitatively predicted at different actuation frequencies by accounting for both static and dynamic effects, as well as external loads, without relying on complex material models and extensive simulation studies. After discussing the design method, experimental validation is presented and performance are evaluated in terms of maximum pressure, maximum flow rate, and energy consumption.