Charmonium dissociation cross sections due to flavor-exchange charmonium-baryon scattering are computed in the constituent quark model. We present results for inelastic J/ψ N and η_c N scattering amplitudes and cross sections into 46 final channels, including final states composed of various combinations of D, D^*, Σ_c, and Λ_c. These results are relevant to experimental searches for the deconfined phase of quark matter, and may be useful in identifying the contribution of initial cc̅

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... to the open-charm final states observed at RHIC through the characteristic flavor ratios of certain channels. These results are also of interest to possible charmonium-nucleon bound states.