OED says: A familiar term for the diligence or public stage-coach of former days. Obs.
1798 J. W. FRERE Loves of the Triangles (Anti-Jacobin) 179 So down thy hill, romantic Ashbourn, glides The Derby dilly, carrying Three Insides.
[Frere’s middle name, as far as I know, is Hookham. No idea what the W. stands for.]
OED also says, for diligence: A public stage-coach. (Now used only in reference to France or other continental countries.)