We report a combined pressure-doping study in the nearly two-dimensional heavy fermion superconductor CeCoIn5 as its superconducting phase is driven to the normal state by Sn doping and/or applied pressure. Temperature-pressure-dependent electrical resistivity measurements were performed at the vicinity of a superconducting quantum critical point where Tc→0. A universal plot of the concentration- and pressure-dependent phase diagram suggests that for the concentrations studied a single mechanism is responsible for reducing Tc and bringing the system to the superconducting quantum critical point. A two-band model with hybridization controlled by pressure and doping provides a consistent description of the phase diagram and the suppression of the d-wave superconductivity in this material.