Emission-line ratios from ions with nearly identical ionization potentials offer a robust solution to the degeneracies inherent to traditional active galactic nuclei (AGNs) metallicity diagnostics. We introduce new semi-empirical metallicity calibrations for the N2O2 and N2S2
Nearby in the stack
diagnostics, explicitly designed to isolate the chemical abundance from the incident radiation field. By coupling an extensive grid of CLOUDY photoionization simulations directly to the intrinsic 2
−
10 keV X-ray luminosity (
LX
) and benchmarking against Seyfert 2 nuclei from the Burst Alert Telescope AGN Spectroscopic Survey (BASS), we establish robust relations valid across the metallicity regime of
8.0≲12+log(O/H)≲9.1
(
0.2≲Z/Z⊙≲2.6
). The
N2O2
and
N2S2
indices trace co-spatial emitting volumes within the narrow-line regions (NLRs), enabling this framework to resolve the significant
LX
-driven systematic biases we previously identified in the standard
N2
and
N2O3
indices. While the
N2O2
ratio proves to be virtually independent of nebular structural variations, the
N2S2
index exhibits a subtle, yet discernible, electron density (
Ne
) susceptibility due to the low critical density (
Nc
) of the [S II]
λλ6716,6731
doublet. Nevertheless, both diagnostics yield highly precise metallicity constraints with tight root-mean-square residual dispersions of
∼0.081
dex for
N2O2
and
∼0.121
dex for
N2S2
. We propose the
N2O2
and
N2S2
calibrations as highly optimized, unbiased metallicity tracers for AGNs.