I can't personally verify either the quote or it's provenance, but, assuming it is indeed legitimate, I'd guess it's from the younger Pinckney because:
It would be interesting to learn which Pinckney made the quote and what, exactly, was the context.
Here is the full quote with source. When read it clearly shows he did not believe that states were ever free and independent, in other words, never sovereign.
Charles Cotesworth Pinckney, South Carolina House of Representatives
18 Jan. 1788Elliot 4:300—302
Gen. Charles Cotesworth Pinckney, in answer to Mr. Lowndes, observed, that, though ready to pay every tribute of applause to the great characters whose names were subscribed to the old Confederation, yet his respect for them could not prevent him from being thoroughly sensible of the defects of the system they had established; sad experience had convinced him that it was weak, inefficient, and inadequate to the purposes of good government; and he understood that most of the framers of it were so thoroughly convinced of this truth, that they were eager to adopt the present Constitution. The friends of the new system do not mean to shelter it under the respectability of mere names; they wish every part of it may be examined with critical minuteness, convinced that the more thoroughly it is investigated, the better it will appear. The honorable gentleman, in the warmth of his encomiums on the old plan, had said that it had carried us with success through the war. In this it has been shown that he is mistaken, as it was not finally ratified till March, 1781, and, anterior to that ratification, Congress never acted under it, or considered it as binding. Our success, therefore, ought not to be imputed to the old Confederation; but to the vast abilities of a Washington, to the valor and enthusiasm of our people, to the cruelty of our enemies, and to the assistance of our friends. The gentleman had mentioned the treaty of peace in a manner as if our independence had been granted us by the king of Great Britain. But that was not the case; we were independent before the treaty, which does not in fact grant, but acknowledges, our independence. We ought to date that invaluable blessing from a much older charter than the treaty of peace—from a charter which our babes should be taught to lisp in their cradles; which our youth should learn as a carmen necessarium, or indispensable lesson; which our young men should regard as their compact of freedom; and which our old should repeat with ejaculations of gratitude for the bounties it is about to bestow on their posterity: I mean the Declaration of Independence, made in Congress the 4th of July, 1776. This admirable manifesto, which, for importance of matter and elegance of composition, stands unrivalled, sufficiently confutes the honorable gentleman’s doctrine of the individual sovereignty and independence of the several states.
In that Declaration the several states are not even enumerated; but after reciting, in nervous language, and with convincing arguments, our right to independence, and the tyranny which compelled us to assert it, the declaration is made in the following words: “We, therefore, the representatives of the United States of America in General Congress assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the name and by the authority of the good people of these colonies, solemnly publish and declare, that these United Colonies are, and of right ought to be, FREE AND INDEPENDENT STATES.” The separate independence and individual sovereignty of the several states were never thought of by the enlightened band of patriots who framed this Declaration; the several states are not even mentioned by name in any part of it,—as if it was intended to impress this maxim on America, that our freedom and independence arose from our union, and that without it we could neither be free nor independent. Let us, then, consider all attempts to weaken this Union, by maintaining that each state is separately and individually independent, as a species of political heresy, which can never benefit us, but may bring on us the most serious distresses.
It is difficult to determine if it is a direct quote:
"Gen. CHARLES COTESWORTH PINCKNEY, in answer to Mr. Lowndes, observed, that, though ready to pay every tribute of applause to the great characters whose names were subscribed to the old Confederation, yet his respect for them could not prevent him from being thoroughly sensible of the defects of the system they had established; sad experience had convinced him that it was weak, inefficient, and inadequate to the purposes of good government; and he understood that most of the framers of it were so thoroughly convinced of this truth, that they were eager to adopt the present Constitution In that Declaration the several states are not even enumerated; but after reciting, in nervous language, and with convincing arguments, our right to independence, and the tyranny which compelled us to assert it, the declaration is made in the following words: "We, therefore, the representatives of the United States of America in General Congress assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the name and by the authority of the good people of these colonies, solemnly publish and declare, that these United Colonies are, and of fight ought to be, FREE AND INDEPENDENT STATES." The separate independence and individual sovereignty of the several states were never thought of by the enlightened band of patriots who framed this Declaration; the several states are not even mentioned by name in any part of it, as if it was intended to impress this maxim on America, that our freedom and independence arose from our union, and that without it we could neither be free nor independent. Let us, then, consider all attempts to weaken this Union, by maintaining that each state is separately and individually independent, as a species of political heresy, which can never benefit us, but may bring on us the most serious distresses."
[Gen. Charles Cotesworth Pinckney, January 18, 1788, in "Debates In The Legislature And In Convention Of The State Of South Carolina, On The Adoption Of The Federal Constitution." Constitution Society]
Mr. Kalamata