  Observations of the emission of the carbon cycle species (C, C+ CO) are
commonly used to diagnose gas properties in the interstellar medium but are
significantly sensitive to the cosmic-ray ionization rate. The carbon-cycle
chemistry is known to be quite sensitive to the cosmic-ray ionization rate,
$\zeta$, controlled by the flux of low-energy cosmic rays which get attenuated
through molecular clouds. However, astrochemical models commonly assume a
constant cosmic-ray ionization rate in the clouds. We investigate the effect of
cosmic-ray attenuation on the emission of carbon cycle species from molecular
clouds, in particular the [CII] 158 $\mu$m, [CI] 609 $\mu$m and CO (J = 1 - 0)
115.27 GHz lines. We use a post-processed chemical model of diffuse and dense
simulated molecular clouds and quantify the variation in both column densities
and velocity integrated line emission of the carbon cycle with different
cosmic-ray ionization rate models. We find that the abundances and column
densities of carbon cycle species is significantly impacted by the chosen
cosmic-ray ionization rate model: no single constant ionization rate can
reproduce the abundances modelled with an attenuated cosmic-ray model. Further,
we show that constant ionization rate models fail to simultaneously reproduce
the integrated emission of the lines we consider, and their deviations from a
physically derived cosmic-ray attenuation model is too complex to be simply
corrected. We demonstrate that the two clouds we model exhibit a similar
average $A_{\rm V, eff}$ -- $n_{\rm H}$ relationship, resulting in an average
relation between the cosmic-ray ionization rate and density $\zeta(n_{\rm H})$.
We conclude by providing a number of implementation recommendations for CRs in
astrochemical models, but emphasize the necessity for column-dependent
cosmic-ray ionization rate prescriptions.
