The very small number of known ferromagnetic superconductors places the study of such compounds at the frontier of superconductivity research. Recently, UCoGe has emerged as a new member of the class of materials exhibiting coexistence of ferromagnetism and superconductivity (Curie temperature TCurie = 3 K; superconducting critical temperature Ts = 0.8 K). This compound has generated much excitement, in part because it has been proposed that the superconductivity derives from spin triplet pairing mediated by ferromagnetic interactions. Therefore, a key question is how changes in the magnetic state of UCoGe affect the superconducting properties. We have carried out a comprehensive study of the UCo1-xFexGe and UCo1-xNixGe series of compounds across the entire range of composition 0 ≤ x ≤ 1. We report the results of x-ray diffraction, electrical resistivity, and magnetization measurements to elucidate the magnetic and superconducting phase diagram of the U[Fe, Co, Ni]Ge system. Substitution of either Ni or Fe into UCoGe initially results in an increase in the Curie temperature. At higher dopant concentrations (x), the ferromagnetic state crosses over to paramagnetism in UCo1-xFexGe and antiferromagnetism in UCo1-xNixGe.