Where would they find gators?
Since the Cherokee were native to the American southeast, I would guess
they found them nearly everywhere there was water. The story of how they
got to where the reservations are is both tragic and one of the more shameful
portions of our national history.
Now, I would guess that they get alligator from farms. You can, too:
http://www.gatorama.com/ribs.htm was the first place that came up
on a Google search. You get get it for less elsewhere, though.
Eric