I would be hard pressed to choose between a .577 Light Nitro (as described by Taylor in 9ThreeXFifty7's post above), a Jeffery .400 (as others have suggested), and a 12-bore Paradox (gatsby's pick, and a passion of mine).

Provided the rifle was lively, properly balanced, and fitted well, and the bullets were bonded-core softs or 20:1 lead alloy, I would be equally happy with any of the above.

The underlying theme here is that with few exceptions, the hypothetical tiger hunter would be happiest with a traditional vintage chambering from the heyday of the Raj. Almost any calibre will kill a tiger, but to truly hunt a tiger one must jolly-well be armed with a pukka rifle!