In addition to the prototypical Ni-Mn-based Heusler alloys, the Co-Ni-Ga systems have recently been suggested as another prospective materials class for magnetic shape-memory applications. We provide a characterization of the dynamical properties of this material and their relation to the electronic structure within a combined experimental and theoretical approach. This relies on inelastic neutron scattering to obtain the phonon dispersion while first-principles calculations provide the link between dynamical properties and electronic structure. In contrast to Ni₂MnGa, where the softening of the TA₂ phonon branch is related to Fermi-surface nesting, our results reveal that the respective anomalies are absent in Co-Ni-Ga, in the phonon dispersions as well as in the electronic structure.