Using subpicosecond optical pump-probe techniques, coherent zone-folded longitudinal acoustic phonons (ZFLAPs) were investigated in an InGaN multiple quantum well structure. A two-pump differential transmission technique was used to generate and control coherent ZFLAP oscillations through the relative timing and amplitude of the two pump pulses. Enhancement and suppression of ZFLAP oscillations were demonstrated, including complete cancellation of generated acoustic phonons for the first time in any material system. Coherent control was used to demonstrate that ZFLAPs are generated differently in InGaN multiple quantum wells than in GaAs/AlAs superlattices.