We numerically study stochastic resonance in the unzipping of a model double-stranded DNA by a periodic force. We observe multiple peaks in stochastic resonance in the output signal as the driving force frequency is varied for different force amplitudes, temperature, chain length, and chain heterogeneity. Multiple peaks point to the existence of multiple stable and metastable states, which correspond to dynamical states of partially zipped and unzipped conformations and transitions between them. We quantify such transitions by looking at the time evolution of the fraction of bound base pairs. We obtain phase diagrams in the force amplitude-temperature plane both in the resonance frequency of the primary peak and the output signal at the peak value. We further obtain an excellent scaling behavior of the output signal for changing lengths of the DNA. Resonance behavior is also affected by chain heterogeneity as it depends strongly on which base pair the periodic forcing is applied.