We study the prospects in the search of dark matter offered by the newly selected NASA MeV mission COSI (Compton Spectrometer and Imager). This instrument is designed and optimized to detect spectral lines, and we show it offers an exquisite possibility to detect dark matter directly decaying or annihilating into monochromatic gamma-rays. This is the case, for example, for axion-like particles (ALPs) which undergo decay into two photons. Furthermore, we show that COSI can lead to important progress in the quest for primordial black holes (PBHs) dark matter, through measurements of the 511 keV line from the positrons produced via Hawking evaporation. We also outline opportunities for the search of continuum signals, such as those expected from sub-GeV dark matter annihilation/decay into leptons and PBH evaporation into photons. We find that also in this case COSI can lead to improvements of current bounds.