There are a few sources that address American pleasure gardens directly:
Blair, John Purdy, Jr. “Productions at Niblo’s Garden Theatre, 1849-1862.” PhD diss., University of Georgia, 1982.
Bloom, Arthur W. “Science and Sensation, Entertainment and Enlightenment: John Mix and the Columbian Museum and Gardens.” Performing Arts Resources 21 (1998): 33-49.
Douglas, Lake. “Pleasure Gardens in Nineteenth-Century New Orleans: ‘Useful for All Classes of Society’.” In The Pleasure Garden, from Vauxhall to Coney Island, edited by Jonathan Conlin. Philadelphia; University of Pennsylvania Press, 2013.
Douglas, Lake. “Certain Pleasures, Ambiguous Grounds: The Etymology and Evolution of the Pleasure Garden” Journal of Landscape Architecture 8, no. 1 (Spring 2013)
Duclow, Geraldine A. “Philadelphia’s Early Pleasure Gardens.” Performing Arts Resources 21 (1998): 1-17.
Eberlein, Harold Donaldson, and Cortlandt Van Dyke Hubbard, “The American ‘Vauxhall’ of The Federal Era,” Pennsylvania Magazine of History and Biography 57 (1944).
Feldman, Benjamin. East in Eden: William Niblo and His Pleasure Garden of Yore. New York: New York Wanderer Press (in association with the Green-Wood Historic Fund), 2014.
Frick, John W. “‘Fireworks, Bonfires, Balloons and More’: New York’s Palace Garden.” Performing Arts Resources 21 (1998): 19-32.
Garrett, Thomas M., “A History of Pleasure Gardens in New York City, 1700-1865.” PhD dissertation, New York University, 1978.
Matheson, Katy, “Niblo’s Garden and its ‘Concert Saloon,’ 1828-1846.” Performing Arts Resources 21 (1998): 53-105.
O’Malley Therese, et al. “Pleasure Ground/Pleasure Garden” in Keywords in American Landscape Design. New Haven: Yale University Press, 2010. 518-24.
Sarudy, Barbara Wells. Gardens and Gardening in the Chesapeake, 1700-1805 (Baltimore: John Hopkins University Press, 1998), chapter 9.
Stubbs, Naomi. “Pleasure Gardens of America: Anxieties of National Identity.” In The Pleasure Garden, from Vauxhall to Coney Island, edited by Jonathan Conlin. Philadelphia; University of Pennsylvania Press, 2013.
Thompson, Jr., George A. “1821: The African Grove.” Chapter 2 in A Documentary History of the African Theatre. Evanston: Northwestern University Press, 1998.
If you know of any sources you would like to be added to this list, please leave a comment below, and I’ll add the reference.