There are 2 titles associated with this firm.

Edgeworth, Maria. The Cherry-Orchard: Also, a Description of the Tiger. New Haven: John Babcock and Son, S. & W.R. Babcock, William M'Carty and Thomas Davis, 1820.
Bray, Anna E. The Talba, or Moor of Portugal. A Romance. By Mrs. Bray, Author of "The White Hoods," "The Protestant," "Fitz of Fitz-Ford," &c. &c. In Two Volumes. New York: James and John Harper [Cliff Street], H.C. Carey and I. Lea, John Grigg, 1831.