We demonstrate that coherent acoustic phonons derived from plasmonic nanoparticles can modulate electronic interactions with proximal excitonic molecular species. A series of gold bipyramids with systematically varied aspect ratios and corresponding localized surface plasmon resonance energies, functionalized with a J-aggregated thiacarbocyanine dye molecule, produces two hybridized states that exhibit clear anticrossing behavior with a Rabi splitting energy of 120 meV. In metal nanoparticles, photoexcitation generates coherent acoustic phonons that cause oscillations in the plasmon resonance energy. In the coupled system, these photogenerated oscillations alter the metal nanoparticle's energetic contribution to the hybridized system and, as a result, change the coupling between the plasmon and exciton. We demonstrate that such modulations in the hybridization are consistent across a wide range of bipyramid ensembles. We also use finite-difference time domain calculations to develop a simple model describing this behavior. Such oscillatory plasmonic-excitonic nanomaterials offer a route to manipulate and dynamically tune the interactions of plasmonic/excitonic systems and unlock a range of potential applications.