For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects are already anticipated at the level of the semi-classical analysis of the Lindblad equation and further supported by the full quantum (numerical) treatment. The system is predicted to exhibit different dynamical phases characterized by an oscillating nonequilibrium steady state with subharmonic periodicity, which is a hallmark of time crystals. We expect that these phases can be directly probed in various cavity QED experiments.