This study investigates coupled orbit-attitude dynamics around asteroids subject to solar radiation pressure and gravity irregularities. The solutions of Sun-synchronous orbits with Sun-tracking attitude motion are analytically derived by applying linearization and averaging. To verify the validity of the analytical solutions, numerical simulations are performed based on non-linear coupled orbit-attitude equations of motion. In addition, the stability of such coupled motion is analyzed using finite-time Lyapunov exponents. It is demonstrated that the Sun-synchronous orbit-attitude coupled motions exhibit long-term stability under certain conditions, and thus, these motions are useful and feasible options for asteroid missions.