Despite having practical applications in battery technology and serving as a model system for Fermi resonance coupling, ethylene carbonate (EC) receives little direct attention as a vibrational probe in nonlinear vibrational spectroscopy experiments. EC contains a Fermi resonance that is well-characterized in the linear spectrum, and the environmental sensitivity of its Fermi resonance peaks could make it a good molecular probe for two-dimensional infrared spectroscopy (2DIR) experiments. As a model system, we investigate the linear and 2DIR vibrational spectrum of the carbonyl stretching region of ethylene carbonate in tetrahydrofuran. The 2DIR spectrum reveals peak dynamics that evolve coherently. We characterize these dynamics in the context of Redfield theory and find evidence that EC dynamics proceed through coherent pathways, including singular coherence transfer pathways that have not been widely observed in other studies. We find that coherent contributions play a significant role in the observed dynamics of cross-peaks in the 2DIR spectrum, which must be accounted for to extract accurate measurements of early waiting time dynamics.