Advanced magnetic shape memory materials like the prototypical Ni-Mn-Ga alloy system are limited to operating temperatures that are too low for many practical applications. To overcome this problem, an intensive search for new magnetic shape memory compounds has been started. One interesting system, showing magnetic as well as conventional shape memory behavior, is CoNi-Ga. In this work we report systematic studies of stoichiometric Co-Ni-Ga based alloys in the full and inverse Heusler structure by means of density functional theory. A prediction of the martensitic transition temperatures can be obtained by the structural energy differences calculated for different crystal structures. In prototype, near-stoichiometric Ni-Mn-Ga, the (pre-)martensitic transformation is accompanied by an anomalous softening of one transversal acoustic phonon branch along the  direction which has been frequently linked to nesting features of the Fermi surface in the past. In order to clarify this aspect for the Co–NiGa system, we will discuss the influence of structure on the phonon dispersions determined from first principles and investigate whether the Fermi surface of the Co-Ni-Ga compound reveals nesting features as well.