A. From: Roger D. Abrahams and Lois Rankin, eds., Counting-Out Rhymes: A Dictionary (University of Texas Press, 1980, p. 195):

465
Queen, queen, Caroline,
Dipped her hair in turpentine,
Turpentine made it shine.
Queen, queen Caroline.

Usually a taunt. Also found as a jump-rope rhyme; see JRR, p. 184 ("Sweet, sweet Caroline").

Bolton (1888), 116 [Edinburgh, Scotland].
Gregor (1891), 11, 24 [Scotland]. Six variants: one begins "Eevil, eevil, eevil-ine"; one, "Eery, ary, areline."
Clinton Johnson (1896), 165. Begins "Engine number nine."
Waugh, JAF, 31 (1918), 46 [Ontario, 1909].
Reid, Misc. of Rymour Club, 1 (1911), 104 [Edinburgh]. Begins "Good Queen Caroline." Ritchie (1965), 40, 47 [Edinburgh]. Two variants.

B. From: Roger D. Abrahams, ed., Jump-Rope Rhymes: A Dictionary (University of Texas Press, 1969, p. 184):

(535)
Sweet, sweet Caroline,
Dipt her face in Terpentine,
Terpentine, made it shine.
Sweet sweet Caroline.

Also a counting-out rhyme.

Douglas (1916), 61 [London].

~Masato