The aerodynamic optimization design of coaxial rotor for tailsitter UAV faces challenges in balancing multiple flight modes and addressing complex aerodynamic interference between rotors. To address these challenges， this study establishes a high-fidelity aerodynamic model based on a hybrid Viscous Vortex Particle Method （VVPM） and Vortex-In-Cell （VIC） approach. A multi-fidelity Bayesian optimization strategy is designed to balance computational costs and accuracy for rotor aerodynamic performance. By treating rotor hover power and forward-flight power as dual optimization objectives， a Pareto optimal solution set for the coaxial rotor design is derived. Flow-field analysis reveals that the hover-optimized design employing mid-span wide chord and gradient twist configurations effectively suppresses blade tip vortex development and enhances hover efficiency. The forward-flight optimized design utilizes inner-span increasing chord and high-gradient twist designs to mitigate forward-flight blade tip vortices and profile drag power and improve propulsive efficiency， yet induces premature vortex roll-up and reduces performance in hover. A balanced optimization design， harmonizing chord gradient and twist angle distributions， synergistically balances hover/forward-flight aerodynamic performance， overcoming limitations of single-condition optimization.