The instability in a horizontal layer of stratified compressible isotropic and anisotropic plasmas has been studied to include simultaneously the effects of Coriolis forces and the finiteness of the ion Larmor radius. Using an integral approach, the dispersion relation has been derived in both cases for plasmas having density stratified exponentially along the vertical. The dispersion relation has been solved numerically and it is found that both the influence of gyroviscosity and Coriolis forces have stabilizing influence on the instability in the isotropic plasmas. The same result is obtained for the case of anisotropic plasmas where also the dispersion relation has been evaluated numerically.