Per my balistic calculator, a .575 ball weighing 285 grs, moving at 1875fps develops 2201 ft/lbs at the muzzle, and would therefore qualify. It would take a much heavier load than what I usually use to get there though. just for fun, here's the data for .50 and .54 RBs too (not exact weights for pure lead).
--.530 230 gr at 2080 fps is good for 2210ft/lbs
--.490 at 180 grs would have to be moving at 2350fps to develop 2207 ft/lbs at the muzzle.
Now for the loads required to achieve this, going by my Lyman manual--since I dont load anywhere near these levels...
.58 cal-- Manual's highest shown velocity was out of a 24" barrell, even though they tested longer ones also,falls a little short as it is "only" 1809fps, but took Lyman 190 grs of Goex FF to get there.
.54 cal--the only barrel lenght that made the required velocity of 2080 fps or above, was a 43" that developed 2113fps with 140grs of Goex FFF, with the heaviest loading shown being 160 grs that developed 2158 fps.
.50 cal--the only load shown that meets or exceeds the 2350 fps required was fired out of a 43" barrel, and was launched with 170 grs of Goex FFF for 2354 fps.
Just as a comparison, a .30 180 gr bullet, such as fired out of a .30-06, also meets this requirement at 2350fps, which most would consider a light load, so I would have to agree with Skylinewatcher in that the rules are very skewed in favor of modern equipment.
I am not suggesting anyone try these loads, just showing them what it would take to get there, at least per the Lyman book and my calculator. Since the OP stated that the requirement was measured my Muzzle Energy, the hunting ranges comment in the second post shouldn't be used against you if you chose to try this hunt. But if anyone actually loads like this to get these type of energy levels out of their rifles, well, you're more of a man than I am as those loads are quite a bit heavier than I load my guns. We all know that the deer loads we use are much lighter. Even the common elk/moose loads that have been posted dont usually approach these velocities, and they all seem to work very well. So I will go out on a limb a bit here, as I have NOT hunted bison so can not speak from experience, but I have some serious doubts about needing that much to take a bison. If anything, I think the extra penetration gained by using a elk/moose level load (of 80-110 grs for a .54--which seems to be common with members here, which includes my 80gr deer load) would have more advantages than playing "mine goes faster than yours".