We analyze the geometry and electronic structure of a series of amorphous Zn-Ir-O systems using classical molecular dynamics followed by density functional theory taking into account two different charge states of Ir (+3 and  +4). The structures obtained consist of a matrix of interconnected metal-oxygen polyhedra, with Zn adopting preferentially a coordination of 4 and Ir a mixture of coordinations between 4 and 6 that depend on the charge state of Ir and its concentration. The amorphous phases display reduced band gaps compared to crystalline ZnIr2O4 and exhibit localized states near the band edges, which harm their transparency and hole mobility. Increasing amounts of Ir in the Ir(4+) phases decrease the band gap further while not altering it significantly in the Ir(3+) phases. The results are consistent with recent transmittance and resistivity measurements.