We establish an account of electromagnetic scattering by coated spheres with radial dielectric and magnetic anisotropy. Within full-wave scattering theory, we show that the total scattering cross section Qs is strongly dependent on both the dielectric anisotropy and magnetic anisotropy. As a consequence, by a suitable adjustment of the radius ratio, one may make the anisotropic coated particle nearly transparent or invisible. In the quasistatic case, we take one step forward to derive the effective permittivity and permeability for the coated particle, and the near-zero scattering radius ratio can be well described within effective medium theory. To one's interest, the introduction of radial anisotropy is helpful to achieve better transparency quality such as a much smaller Qs and wider range of near-zero scattering ratio. Moreover, when the coated particle is anisotropic, the position of the near-zero scattering radius ratio can be tunable, resulting in a tunable electromagnetic cloaking.