We revisit a singlet Majoron model in which neutrino masses arise from the spontaneous violation of lepton number. If the Majoron obtains a mass of order MeV, it can play the role of dark matter. We discuss constraints on the couplings of the massive Majoron with masses of order MeV to neutrinos from supernova data. In the dense supernova core, Majoron-emitting neutrino annihilations are allowed and can change the signal of a supernova. Based on the observation of SN1987A, we exclude a large range of couplings from the luminosity and the deleptonization arguments, taking the effect of the background medium into account. If the Majoron mass does not exceed the Q-value of the experiment, the neutrino-Majoron couplings allow for neutrinoless double beta decay with Majoron emission. We derive constraints on the couplings for a Majoron mass of order MeV based on the phase space suppression and the diminishing signal-to-background ratio due to the Majoron mass. The combination of constraints from astrophysics and laboratory experiments excludes a large range of neutrino-Majoron couplings in the mass range of interest for Majoron dark matter, where they complement existing cosmological bounds from dark matter stability and the effects of a decaying Majoron on the cosmic microwave background anisotropy spectrum.