On 29 May 1744 the General Assembly of South Carolina passed a rather curious [act.] (https://books.google.com/books?id=ZIE2AQAAMAAJ&pg=PA188&dq=%22south+carolina%22&hl=en&sa=X&ved=0ahUKEwi5mY6a-PvYAhVkUt8KHRdlCn0Q6AEIKTAA#v=onepage&q&f=false)
Forasmuch as it is become neceſſary to give ſome Encouragement, to have Beaſts of Prey deſtroyed, which of late have been very deſtructive to the Stocks of Cattle, Sheep, and Hogs in this Province . . . . be it enacted . . . . That all and every Perſon and Perſons whoever, that ſhall hereafter kill in this Province . . . . any of the Beaſts of Prey herein after mentioned, ſhall have the following Rewards, that is to ſay,
For a Tyger, Eight Shillings.
For a Wolf, Six Shillings.
For a Bear, Four Shillings.
For a wild Cat, Four Shillings.
So what was going on here? Did the South Carolina legislators believe there was a population of Panthera Tigris roaming the woods outside Charleston? Or did "Tyger" then refer to some other sort of critter, like a cougar/puma/mountain lion? (One more name never hurt a cat.)
There are no documented tiger species in N. America, at least not in modern history.
But interestingly, "Tyger" does seem to be a something unique from Panthers (Mountain Lions), or "wild Cat" (which is a Bobcat).
Between 1700 and 1709 John Lawson traveled the South Carolina backcountry, and published A New Voyage to Carolina documenting his travels. He includes a section and a few illustrations on beasts that he encountered.
He had the following to say of "Tygers":
Tygers are never met withal in the Settlement; but are more to the Westward, and are not numerous on this Side the Chain of Mountains. I once saw one, that was larger than a Panther, and seem'd to be a very bold Creature. The Indians that hunt in those Quarters, say, they are seldom met withal. It seems to differ from the Tyger of Asia and Africa.
Oddly, he also tells that numerous Native Americans recount a large cat, similar in color to the panther, which is unable to climb trees and absolutely terrifies them.
I have been inform'd by the Indians, that on a Lake of Water towards the Head of Neus River, there haunts a Creature, which frightens them all from Hunting thereabouts. They say, he is the Colour of a Panther, but cannot run up Trees; and that there abides with him a Creature like an Englishman's Dog, which runs faster than he can, and gets his Prey for him. They add, that there is no other of that Kind that ever they met withal; and that they have no other way to avoid him, but by running up a Tree. The Certainty of this I cannot affirm by my own Knowledge, yet they all agree in this Story. As for Lions, I never saw any in America; neither can I imagine, how they should come there.
While he specifically mentions that he has not seen one, he does mention he has not seen anything resembling a Lion - which hints that their description had similarities.
It is possible, even likely, they were referring to a Mountain Lion in this context - but the term was used to describe a different creature during the period. That's about the best I can do.