Measurements of hyperfine polarization quantum beats are used determine the magnetic dipole (A) and electric quadrupole (B) coupling constants in the excited atomic Cs 8p level. The experimental approach is a novel combination of pulsed optical pumping and time-delayed stimulated emission probing of the excited level. From the measured evolution of the atomic linear polarization degree as a function of probe delay time, we determine the hyperfine coupling constants A = 7.42(6) MHz and B = 0.14(29) MHz.