Skillful representation of tropical variability and diurnal cycle of precipitation has remained a challenge in global atmosphere models, and often improvements in the variability lead to degradation in the mean-state. Here, we introduce a configuration of the E3SM Atmosphere Model with a new microphysics scheme and several enhancements to the deep convective scheme that improves the variability while keeping the mean-state climatology largely unchanged. The new configuration improves various modes of convectively-coupled equatorial waves, with increased strength of Kelvin waves and more coherent eastward propagation of the Madden Julian Oscillation from the Indian Ocean to the central Pacific Ocean. The same configuration also improves both the phase and amplitude of the diurnal cycle of precipitation, particularly over the continental United States in the boreal summer and over Tropical land regions. Previous studies have shown that, individually taken, some of the deep convective enhancements can improve certain aspects of the variability, and here we show that combining their effects can lead to robust improvements in the variability. This model configuration can form the basis for future studies to examine the response of tropical and diurnal variability under various climate states and their relationships with other modes of variability.