The study underscores the growing importance of considering nonlinear effects in the design of mechanical structures, showcasing applications in micro-mechanical resonators, sensors, gyroscopes, and beyond. Despite recent advancements in Reduced Order Models (ROMs) for studying high-dimensional systems, tailoring a system's nonlinear response remains challenging. Existing optimization strategies often rely on time domain simulations, harmonic balance, or surrogate quantities of the system's nonlinearity, lacking a direct link between the objective function and the system's backbone curve. To address this gap, we propose a novel approach using Lyapunov Subcenter Manifolds (LSMs) to optimize the conservative backbone curve of generic mechanical systems. Unlike existing strategies, this approach targets the backbone curve directly, providing a unique and efficient tool for optimizing nonlinear responses in mechanical systems. LSMs offer advantages such as an analytic expression for the backbone curve, which allows an analytical computation of the sensitivities. Moreover, the LSM yields a minimum-size representation of the system, thus increasing the overall computational efficiency. We also discuss the critical role of robust ROMs and solution methods in optimization processes, which should be as independent as possible from user inputs. The validity of the approach is demonstrated through examples of mechanical structures described by a set of parameters used as design variables in the optimization. Overall, the work contributes a valuable strategy for optimizing nonlinear responses in mechanical systems, with potential applications in various fields.