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We complete our derivation of upper limits on the CP violating $\eta\pi\pi$and $\eta'\pi\pi$ couplings from an analysis of their two-loop contributions tothe neutron electric dipole moment (nEDM). We use a phenomenological Lagrangianapproach which is formulated in terms of hadronic degrees of freedom - nucleonsand pseudoscalar mesons. The essential part of the Lagrangian contains the CPviolating couplings between $\eta(\eta')$ and pions. Previously, we includedphotons using minimal substitution in case of the proton and charged pions. Nowwe extend our Lagrangian by adding the nonminimal couplings, i.e. anomalousmagnetic couplings of nucleons with the photon. The obtained numerical upperlimits for the $\eta\pi\pi$ and $\eta'\pi\pi$ couplings$|f_{\eta\pi\pi}(M_\eta^2)|<4.4 \times10^{-11}$ and$|f_{\eta^\prime\pi\pi}(M_{\eta'}^2)|<3.8 \times10^{-11}$ can be useful for therelated, planned experiments at the JLab Eta Factory. Using presentexperimental limits on the nEDM, we derive upper limits on the CP violating$\bar\theta$ parameter of $\bar{\mathrm{\theta}}<4.7 \times 10^{-10}$.

Updated limits on the CP violating $\eta\pi\pi$ and $\eta'\pi\pi$ couplings derived from the neutron EDM