Green’s Dictionary of Slang

coachman’s seat n.

[? a coachman is seated behind]

a bustle or dress improver.

[UK]Leamington Spa Courier 27 Sept. 7/4: Enormities of Fashion [...] that ‘moveable coachman’s seat,’ ordinarily called crinolette. It is growing and growing.
[Aus]Bulletin (Sydney) 4 Jul. 12/2: There were two burly bushies from the back Barcoo, and had dumped themselves down in the same tram-compartment as a Redfern lady whose ‘coachman’s seat,’ or improver, stuck out as stiff and fierce as a snub-nosed man in a hot theological argument.