Coherent multidimensional optical spectroscopy is an emerging technique for resolving structure and ultrafast dynamics of molecules, proteins, semiconductors, and other materials. A current challenge is the quality of kinetics that are examined as a function of waiting time. Inspired by noise-suppression methods of transient absorption, here we incorporate shot-by-shot acquisitions and balanced detection into coherent multidimensional optical spectroscopy. We demonstrate that implementing noise-suppression methods in two-dimensional electronic spectroscopy not only improves the quality of features in individual spectra but also increases the sensitivity to ultrafast time-dependent changes in the spectral features. Measurements on cresyl violet perchlorate are consistent with the vibronic pattern predicted by theoretical models of a highly displaced harmonic oscillator. The noise-suppression methods should benefit research into coherent electronic dynamics, and they can be adapted to multidimensional spectroscopies across the infrared and ultraviolet frequency ranges.