Antisite defects in ZnSe, ZnSe and SeZn in the neutral and +1 charge states, are found to possess some favorable attributes to be spin-based qubits. Systematic density functional theory calculations utilizing hybrid exchange-correlation functionals were performed to investigate the optical signatures and formation energies of these defects. Defect level diagrams, configuration coordinate diagrams, and transition dipole moments of possible internal optical transition paths of these antisites were calculated and compared to those of the nitrogen-vacancy center in diamond. The antisite defects are not found to be the most predominant native defects based on the formation energy diagrams for relevant conditions of compound stability. Nevertheless, there may be non-equilibrium routes to realize these defects as some formation energies are not unreasonably high.