We propose and model a method to excite a large number of coherent magnons with high momentum in optical cavities. This is achieved by two counterpropagating optical modes that are detuned by the frequency of a selected magnon, similar to stimulated Raman scattering. In submillimeter-size yttrium iron garnet spheres, a milliwatt laser input power generates 106-108 coherent magnons. The large magnon population enhances Brillouin light scattering, a probe suitable to access their quantum properties.