Let me try & address the various issues here.

1 I mentioned the debate about the Cheetah (the cat) possibly being introduced by Moghul kings in the 12th or 13th century for hunting Black Buck etc. There are some historical paintings of the Cheetah but none that I know of before the 12th Century. There are historical records of lions, tigers & leopards from 5000 years ago.
2 The Chital (the deer) is native to India & Sri Lank. These animals inhabited mostly desiduous forests with grass clearings up to about 4000 feet elevation. (The reference book "Mammals of India by SH Prater" is a classic that includes information from the early 19th century. I also have personal copies of Sanderson (1880s)& Dunbar Brander (1910) which are collectors' items.) My point is that the deer were introduced into new habitat that was not their original home by some kings. Sariska sanctuary is one good example - the Maharaja introduced chital deer into this hunting preserve about 100 years ago.
3 Hunting in India is a very complex issue. My dad was in the Forestry & wildlife department since 1946 & retired in 1983. He was once Chief wildlife warden of Tamil Nadu state. I had the opportunity to travel widely to various forest reserves, sanctuaries & national parks since the late 1950's. The population density is so high & encroachment of habitat is so severe that the total forest area is now only about 10% of total land area, including the himalayas. In the peninsular regions this is much less. Even in remote areas like Mundanthurai sanctuary, Mudumalai sanctuary, Annamalai (Indira Gandhi) national park etc. the proximity of villages, major roads, exposure to cattle borne diseases, etc. are a major issue. Poaching is still common. In some areas the villagers tap high voltage lines & electrocute crop raiding animals including elephants. I would love to see legalised & controlled hunting being introduced in India again. I am just pesimistic that controlling the hunting effectively is impossible as the various government agencies do not have the resources or skills. The cost of effectively controlling the legal hunting would be prohibitive. Illegal poaching would become a lot worse becasue of the informal networks of political patronage which would protect such perpetrators. For example the Nawab of Pataudi (former Indian cricket captain) was arested a few years ago with a shotgun, rifle, black buck carcass etc. in his car. Even though the offfence is a non-bailable one (for killing a protected animal), the case is still in court & he is free. I believel that the case will ultimately come to nothing or one of his servants will get a minor conviction! Check these sites or Google "Pataudi+poaching". http://www.google.co.nz/search?hl=en&rlz=1T4GGLJ_enNZ222NZ237&q=Pataudi%2Bpoaching&meta=

4 It is so difficult to get ammunition legally in most parts of India. Again, you need the right contacts.