We describe internal, low-frequency variability in a 21-year simulation with a cloud-resolving model. The model domain is the length of the equatorial Pacific and includes a mixed-layer ocean, which permits coherent cycles of sea surface temperature (SST), atmospheric convection, and the convectively coupled circulation. The warming phase of the cycle is associated with near-uniform SST, less organized convection, and sparse low cloud cover, while the cooling phase exhibits strong SST gradients, highly organized convection, and enhanced low cloudiness. Both phases are quasi-stable but, on long timescales, are ultimately susceptible to instabilities resulting in rapid phase transitions.   The internal cycle is leveraged to understand the factors controlling the strength and structure of the tropical overturning circulation and the stratification of the tropical troposphere. The overturning circulation is strongly modulated by convective organization, with SST playing a lesser role. When convection is highly organized, the circulation is weaker and more bottom-heavy. Alternatively, tropospheric stratification depends on both convective organization and SST, depending on the vertical level. SST-driven variability dominates aloft while organization-driven variability dominates at lower levels. A similar pattern is found in ERA5 reanalysis of the equatorial Pacific. The relationship between convective organization and stratification is explicated using a simple entraining plume model. The results highlight the importance of convective organization for tropical variability and lay a foundation for future work using coupled, idealized models that explicitly resolve convection.