  In the supersymmetric models, the dominant sources of the hadronic
flavor-diagonal CP violation at low energy are the theta term and the
chromoelectric dipole moments of quarks. Using QCD sum rules, we estimate the
preferred range and the best values for the CP-odd meson-nucleon coupling
constants induced by these operators. When the theta term is removed by the
axion mechanism, the size of the most important isospin triplet pion-nucleon
coupling is estimated to be \bar g_{\pi NN}^{(1)} = 2 times 10^{-12}(tilde d_u
- tilde d_d), where chromoelectric dipole moments are given in units of
10^{-26} cm.
