Single longitudinal-mode Brillouin fiber lasers are very promising for many applications, such as coherent optical communication, interferometric sensing, coherent radar detection, and microwave photonics. In the lasers with doublyresonant cavities Stokes wave is generated by a short fiber ring cavities that are simultaneously resonant for pump and Stokes radiation. Therefore, such lasers emit coherent light in two laser lines separated by the Brillouin shift. We report a simple procedure allowing precise adjustment of the Brillouin fiber ring cavities for doubly-resonant operation and demonstrate two completely passive solutions enabling perfect stabilization of such cavities for generation of doublefrequency light. In our experiments, the first laser configuration is stabilized through self-injection locking mechanism implemented to the laser cavity with DFB semiconductor pump laser. Second configuration comprises a nonlinear fiber mirror based on the population inversion dynamical gratings induced in low-absorbed Er-doped fiber. The pump-toStokes conversion efficiency of ~40% in both cases and the Stokes linewidth of <500Hz for the first case and < 100Hz for the second are successfully demonstrated.