We present a detailed theoretical study of chiral topological superconductor phases in proximity-superconducting graphene systems based on an effective model inspired by density functional theory simulations. Inducing s-wave superconductivity in quantum anomalous Hall effect systems leads to chiral topological superconductors. For out-of-plane magnetization we find topological superconducting phases with even numbers of chiral Majorana fermions per edge, which is correlated with the opening of a nontrivial gap in the bulk system in the K points and their connection under particle-hole symmetry. We show that in a quantum anomalous Hall insulator with in-plane magnetization and a nontrivial gap opening at M, the corresponding topological superconductor can be tuned to host only single chiral Majorana states at its edge, which is promising for proposals exploiting such states for braiding operations.