We investigate the design of an active support system for the thin primary mirror of a mid-sized telescope system used for optical satellite communication and space debris observation. To handle the complexity of this task, a general design methodology is proposed. The design for the axial and lateral support is separated into several subtasks to reduce the number of design variables in every design step. Due to the independence of mirror geometry and material, this methodology is also applicable to larger mirrors. Utilizing the proposed procedure, an active support for a 1-m meniscus mirror with 25 mm thickness and the requirement to achieve diffraction-limited optical performance is developed. The final system consists of 32 axial and 8 lateral actuators supporting the mirror with a maximal simulated RMS error of 8.8 nm and PV error of 48.0 nm when pointing to zenith. Simulations show that the obtained design ensures the required performance even under commonly occurring mirror deformations.