Eumelanin, the human skin pigment, is a poly-indolequinone material possessing a unique combination of physical and chemical properties. For numerous applications, the conductivity of eumelanin is of paramount importance. However, its hydration dependent conductivity is not well studied using transport-relaxation methods. Furthermore, there is no such work taking into account the simultaneous control of humidity as well as metal ion concentration. Here we present the first such study of the transport and relaxation characteristics of synthetic eumelanin doped with various Cu ion concentrations while controlling the humidity with a frequency range of 10-3 Hz-1 MHz. We found that Cu ions do not cause the appearance of additional relaxation processes, but partially slow down those present in neat eumelanin. In addition, considering previously published work, the key relaxation process observed in doped and undoped materials is associated with the moisture-induced synthesis of uncharged semiquinones and a corresponding increase in the overall aromaticity of the material.