A special 2-m Ring Solar Telescope (2-m RST) is to be built by YNAO-Yunnan Astronomical Observatory, Kunming, China. Its distinct primary mirror is distinctively shaped in a ring with an outer diameter of 2.02 m and a ring width of 0.35 m. Careful calculation and optimization of the mirror support pattern have been carried out first of all to define optimum blank parameters in view of performance balance of support design, fabrication and cost. This paper is to review the special consideration and optimization of the support design for the unique ring mirror. Schott zerodur is the prevailing candidate for the primary mirror blank. Diverse support patterns with various blank thicknesses have been discussed by extensive calculation of axial support pattern of the mirror. We reached an optimum design of 36 axial supports for a blank thickness of 0.15 m with surface error of ~5 nm RMS. Afterwards, lateral support scheme was figured out for the mirror with settled parameters. A classical push-and-pull scheme was used. Seeing the relative flexibility of the ring mirror, special consideration was taken to unusually set the acting direction of the support forces not in the mirror gravity plane, but along the gravity of the local virtual slices of the mirror blank. Nine couples of the lateral push-pull force are considered. When pointing to horizon, the mirror surface exhibits RMS error of ~5 nm with three additional small force couples used to compensate for the predominant astigmatism introduced by lateral supports. Finally, error estimation has been performed to evaluate the surface degradation with introduced errors in support force and support position, respectively, for both axial and lateral supports. Monte Carlo approach was applied using unit seeds for amplitude and position of support forces. The comprehensive optimization and calculation suggests the support systems design meet the technic requirements of the ring mirror of the 2-m RST.