Graphene nanoribbons support a variety of electronic phases that can be tuned via external stimuli. In particular, zigzag graphene nanoribbons exhibit an antiferromagnetic insulating ground state which can transition to a half-metallic phase under a transverse electric field or when embedded in hexagonal boron nitride. Here, we develop a simple model of a heterostructure composed of a half-metallic zigzag graphene nanoribbon coupled with an Ising superconductor. We demonstrate that an Ising superconductor's s-wave spin-singlet pairing gap component can induce a spin-triplet, odd-parity pairing gap in the half-metallic phase of the nanoribbon via proximity coupling. The resulting superconducting phase is topologically nontrivial, with gate-tunable transitions that enable the emergence of Majorana zero modes.