The integration of a nitrogen cycle represents a recent advancement in Earth system models (ESMs). However, diverse formulations introduce uncertainty in the nitrogen effect on the carbon cycle, leaving the global carbon-nitrogen coupling effect unclear. In this study, we present CNit v1.0, a newly developed carbon-nitrogen cycle model designed for integration with MAGICC (Model for the Assessment of Greenhouse Gas Induced Climate Change), a widely used reduced-complexity model. CNit v1.0 has been calibrated to two land surface models (CABLE and OCN) and (the land component of) a set of Coupled Model Intercomparison Project Phase 6 (CMIP6) ESMs. CNit v1.0 is able to capture the dynamics of the more complex models' carbon-nitrogen cycle at the global-mean, annual scale. The emulation results suggest a consistent nitrogen limitation on net primary production (NPP) in CMIP6 ESMs, persisting throughout the simulations (i.e., over the period 1850-2100) in most models. The emulation provides a way to disentangle diverse nitrogen effects on carbon pool turnovers in CMIP6 ESMs, with our results suggesting that nitrogen deficiency generally inhibits litter production and decomposition while enhancing soil respiration (from a multi-model mean perspective). However, this disentanglement is limited due to a lack of simulations from CMIP6 ESMs which would allow us to fully separate the nitrogen and carbon responses. The results imply a potential reduction in land carbon sequestration in the future due to nitrogen deficiency. Future studies will use CNit to further investigate the carbon-nitrogen coupling effect, including uncertainty, in future climate projections.