We demonstrate the first successful attempt to partially substitute Cu into the Mn3AgN-antiperovskite system to form Mn3Ag(1-x)Cu(x)N thin films with ultra-low temperature coefficient of resistance (TCR) for fabrication of ultra-precise passive components. Films were grown by reactive magnetron sputtering on alumina and glass substrates and were found to be amorphous in nature with highly negative TCR of -233 to -351ppm/˚C in their as-grown state. Increasing Cu alloying from x=0 to 1, resulted in increased sheet resistance, a negative shift of TCR and a change of grain morphology from spherical to elongated. Post-deposition heat treatment at 300-375˚C, resulted in a positive shift of TCR and an ultra-low TCR of -4.66ppm/˚C for films with x=0.6. The heat treatment induces grain growth, surface roughness and the formation of a manganese oxide upper surface layer up until temperatures of 350˚C, after which surface oxidation begins to dominate. The growth rate of the surface layer is controlled by the Cu concentration and heat treatment temperature, which both play a central role in the development of these novel ultra-low TCR Mn3Ag(1-x)Cu(x)N thin film structures.