Engineering applications like drivetrains in stationary and mobile applications suffer from torsional vibrations excited by torque fluctuations from various sources like reciprocating engines and compressors. These vibrations impact the structural integrity of the driveline components and result in undesirable noise emissions. Established countermeasures to mitigate torsional vibrations include vibration dampers and elastic couplings. Regarding the couplings’ torsional stiffness, there is a fundamental conflict of objectives: On the one hand, the stiffness must be high enough to transmit the nominal static torque between the motor and the driven equipment at a reasonable twisting angle while, on the other hand, the coupling should be as flexible as possible to prevent the transmission of torque fluctuations. This can be achieved by a nonlinear coupling element with high initial stiffness followed by an operating range of quasi-zero stiffness. Such a nonlinear torsional coupling can be realized by combining a conventional linear coupling element with a constant positive torsional stiffness and a nonlinear coupling element with a negative torsional stiffness. This paper presents a method to design a nonlinear coupling element with quasi-zero stiffness. The design of the compliant mechanism is based on the post-buckling behavior of cantilevered beams which is simulated using a collocation-based method. The predicted characteristics of the mechanism are compared to experimental measurements. Finally, a case study of a reciprocating engine reveals a reduction of the torsional drive-train amplitudes by up to 93% using a compliant quasi-zero stiffness coupling.