To accelerate the design and discovery of novel functional materials, here, p-type transparent conducting oxides, an inverse design approach is formulated, integrating three steps: i) articulating the target properties and selecting an initial pool of candidates based on design principles, ii) screening this initial pool by calculating the selection metrics for each member, and iii) laboratory realization and more-detailed theoretical validation of the remaining best-of-class materials. Following a design principle that suggests using d5(5) cations for good p-type conductivity in oxides, the Inverse Design approach is applied to the class of ternary Mn(II) oxides, which are usually considered to be insulating materials. As a result, Cr2MnO4 is identified as an oxide closely following selection metrics of thermodynamic stability, wide-gap, p-type dopability, and band-conduction mechanism for holes (no hole self-trapping). Lacking an intrinsic hole-producing acceptor defect, Li is further identified as a suitable dopant. Bulk synthesis of Li-doped Cr2MnO4 exhibits at least five orders of magnitude enhancement of the hole conductivity compared to undoped samples. This novel approach of stating functionality first, then theoretically searching for candidates that merits synthesis and characterization, promises to replace the more traditional non-systematic approach for the discovery of advanced functional materials.