Isn't this (Click here for lyrics & MIDI) the song? It was Peggy who sat in her low-back'd car, though. Sheet music is in the Levy Collection (unfortunately, its images can't come up):

Title: The Low Back'd Car. A Characteristic Irish Song As Given by the Author in His Irish Evenings.
Composer, Lyricist, Arranger: Written and Composd by Samuel Lober.
Publication: New York: Firth & Hall, No.1 Franklin Sq., 1846.
Form of Composition: strophic
Instrumentation: piano and voice
First Line: When first I saw sweet Peggy, 'Twas on a market day
Plate Number: 4058
Subject: Carts & wagons
Subject: Courtship & love
Subject: Weddings
Call No.: Box: 061 Item: 055

Song sheet (Title: Song Sheet Low Back'd Car. / Composer, Lyricist, Arranger: na / Publication: Philadelphia: T.M. Scroggy, 443 Vine St., below 13th, n.d.) is HERE.

~Masato