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The goal of this study is to tune the design of the absorber detector of a Compton camera for prompt γ-ray imaging during ion beam therapy. The response of the Compton camera to a photon point source with a realistic energy spectrum (corresponding to the prompt γ-ray spectrum emitted during the carbon irradiation of a water phantom) is studied by means of Geant4 simulations. Our Compton camera consists of a stack of 2 mm thick silicon strip detectors as a scatter detector and of a scintillator plate as an absorber detector. Four scintillators are considered: LYSO, NaI, LaBr3 and BGO. LYSO and BGO appear as the most suitable materials, due to their high photo-electric cross-sections, which leads to a high percentage of fully absorbed photons. Depth-of-interaction measurements are shown to have limited influence on the spatial resolution of the camera. In our case, the thickness which gives the best compromise between a high percentage of photons that are fully absorbed and a low parallax error is about 4 cm for the LYSO detector and 4.5 cm for the BGO detector. The influence of the width of the absorber detector on the spatial resolution is not very pronounced as long as it is lower than 30 cm.