We report on the thermally excited resonance vibrations of mesoscopic poly(methylmethacrylate)-poly(n-butylacrylate) (PMMA-PnBA) random copolymer colloidal spheres with varying nBA volume fractions. All systems but the bulk PnBA are in the glassy state at room temperature. Brillouin light scattering (BLS), dielectric spectroscopy (DS), and standard polymer characterization techniques reveal the homogeneity of this copolymer system down to the segmental length scale. Theoretical density-of-suites calculations allow the determination of the shear modulus of the copolymer latex spheres from their eigenvibration BLS spectra. The representation of the copolymer longitudinal modulus by Wood's law, combining the PM M A and PnBA homopolymers values, succeeds if a higher fictive "glassy PnBA" modulus instead of the actual modulus of the neat PnBA rubber at room temperature is assumed. This is justified by the dynamic homogeneity of these copolymers exhibiting a single a-relaxation. A facile tuning of the thermo-mechanical properties of latex spheres via the copolymer composition as well as their experimental determination at a single sphere level becomes feasible.