Ternary CxNyOz compounds are actively researched as novel high energy density and ultrahard materials. Although some synthesis work has been performed at ambient conditions, very little is known about the high pressure chemistry of of CxNyOz compounds. In this work, first-principles variable-composition evolutionary structure prediction calculations are performed with the goal of discovering novel mixed CxNyOz materials at ambient and high pressure conditions. By systematically searching ternary variable composition crystalline materials, the full ternary phase diagram is constructed in the range of pressures from 0 to 100 GPa. The search finds the C2N2O crystal containing an extended covalent network of C, N, and O atoms, having space group symmetry Cmc2(1), and stable above just 10 GPa. Several other novel metastable (CO)(x)-(N)(y) crystalline compounds discovered during the search, including two polymorphs of C2NO2 and two polymorphs of C3N2O3 crystals, are found to be energetically favorable compared to polymeric carbon monoxide (CO) and nitrogen. Predicted new compounds are characterized by their Raman spectra and equations of state.