A hybrid approach is proposed to efficiently design a constant elevation-beamwidth beamforming with concentric ring arrays (CRAs). The design exploits the degrees of freedom of the array geometry for superior performance. In particular, the ring radii and the beamformer coefficients are optimized simultaneously for all frequencies. We introduce a convex quadratic programming problem for a given CRA configuration, directly optimizing the beamformer coefficients while maintaining constant elevation-beamwidth over a wide range of frequencies. The proposed objective function contains a control variable, allowing a tradeoff between the directivity factor and the white noise gain. Subsequently, a hybrid approach is proposed to optimize the ring radii with a genetic algorithm exploiting the partial convexity of the problem. Experimental results demonstrate the flexibility and advantages of the proposed approach compared to the state-of-the-art in terms of directivity factor, white noise gain, sidelobe level, and beamwidth consistency, with reduced resources and a significantly lower computation time.