A dual-beam coherent feeding system design approach with a non-uniform layout on a concentric ring array is described and synthesized. In this case, the feeding system is based on a reconfigurable topology composed of a set of alternated power dividers and combiners, providing coherent in-phase outputs. Thus, in this paper, a two-beam architecture based on a coherent feeding system formed by a set of intercalated input signals feeding each circular ring in a non-uniform antenna array with multi-beam shaping and steering features is analyzed. The task of optimizing the aperiodic layout on the shared aperture based on the radii of the circular rings is realized by the differential evolution method. Numerical experiments grounded in antenna synthesis validate the capabilities and improved performance of the proposed dual-beam configuration with a non-uniform layout in contrast with its uniform counterpart, with enhanced performance on average by up to −6.1 dB for sidelobe level and 3.5 dB for directivity. Additionally, the results show a significantly less complex two-beam feeding network in contrast with the case of a typical electronically scanned array—in this proposal, each direction of maximum radiation is conformed and scanned with approximately half of the control inputs.