If we get one deer, and no other ungulates: northern red muntjac (deals with the severe underrepresentation of ungulates from India and China, gives a smaller ungulate to Southeast Asia, morphologically unique, common in zoos, mixes well with several in-game animals, interesting vocalizations.)
If we get one deer, but we also get a blackbuck or other Indian antelope species: either still the muntjac or Pere David's deer (with an antelope at least giving one mid-sized ungulate to India, I'd go for the unique habitat and conservation story of this beautiful icon for China).
Not a lot of demand for Indian deer but the barasingha, hog deer and Eld's deer would all make great choices to go with the rhino, water buffalo, etc. For India, the barasingha is a huge conservation icon, similar to Pere David's in China (but without as strong a zoo angle). Hog deer, on the other hand, are a conservation crisis that gets little attention. From being the most abundant deer species of northern India, hog deer have quietly disappeared from much of their range. Axis deer (more generalist) and sambar still do well but the hog deer has suffered.
If support continues for a long time, then I'd say a pudu is most interesting for me out of the non-Asian deer.