The methane (CH₄) cycle is a key component of the Earth system that links planetary climate, biological metabolism, and the global biogeochemical cycles of carbon, oxygen, sulfur, and hydrogen. However, currently lacking is a numerical model capable of simulating a diversity of environments in the ocean, where CH₄ can be produced and destroyed, and with the flexibility to be able to explore not only relatively recent perturbations to Earth's CH₄ cycle but also to probe CH₄ cycling and associated climate impacts under the very low-O₂ conditions characteristic of most of Earth's history and likely widespread on other Earth-like planets. Here, we present a refinement and expansion of the ocean–atmosphere CH₄ cycle in the intermediate-complexity Earth system model cGENIE, including parameterized atmospheric O₂–O₃–CH₄ photochemistry and schemes for microbial methanogenesis, aerobic methanotrophy, and anaerobic oxidation of methane (AOM). We describe the model framework, compare model parameterizations against modern observations, and illustrate the flexibility of the model through a series of example simulations. Though we make no attempt to rigorously tune default model parameters, we find that simulated atmospheric CH₄ levels and marine dissolved CH₄ distributions are generally in good agreement with empirical constraints for the modern and recent Earth. Finally, we illustrate the model's utility in understanding the time-dependent behavior of the CH₄ cycle resulting from transient carbon injection into the atmosphere, and we present model ensembles that examine the effects of atmospheric pO₂, oceanic dissolved $SO_4^{2-}$ and the thermodynamics of microbial metabolism on steady-state atmospheric CH₄ abundance. Future model developments will address the sources and sinks of CH₄ associated with the terrestrial biosphere and marine CH₄ gas hydrates, both of which will be essential for comprehensive treatment of Earth's CH₄ cycle during geologically recent time periods.