We report on identification and control of important non-radiative recombination centers in GaNP coaxial nanowires (NWs) grown on Si substrates, in an effort to significantly increase light emitting efficiency of these novel nanostructures promising for a wide variety of optoelectronic and photonic applications. A point defect complex, labeled as DD1 and consisting of a P atom with a neighboring partner aligned along a crystallographic <111> axis, is identified by optically detected magnetic resonance as a dominant non-radiative recombination center that resides mainly on the surface of the NWs and partly at the hetero-interfaces. The formation of DD1 is found to be promoted by the presence of nitrogen and can be suppressed by reducing the strain between the core and shell layers, as well as by protecting the optically active shell by an outer passivating shell. Growth modes employed during the NW growth are shown to play a role. Based on these results, we identify the GaP/GaNyP1-y/GaNxP1-x (x<y) core/shell/shell NW structure, where the GaNyP1-y inner shell with the highest nitrogen content serves as an active light-emitting layer, as the optimized and promising design for efficient light emitters based on GaNP NWs.