(Oxford English Dictionary)
b. 'A street-car having a second floor and seats on top; a freight- or cattle-car with two floors' (Cent. Dict.). Also, a double-decked omnibus. orig U.S.
1867 Terr. Enterprise (Virginia, Nev.) 19 July 3/1 A 12-mule double-decker prairie schooner. 1878 Design & Work IV. 324/3 [Quoting U.S. newspaper] The car is a double-decker. 1887 Harper's Mag. Sept. 557/2 The street-cars are double-deckers, with seats upon the roof as well as within. 1895 Popular Sci. Monthly Apr. 757 The 'double decker' or two-story cars.
16 November 1876, New York Times, pg. 8:
A "DOUBLE DECK" CAR.
Within a few days the Sixth Avenue Railroad Company have put upon their line what is known as a "double-deck" car, that is, a car with seats placed on the roof, which are reached by a circular stairway from either platform. The roof is further provided with a towering awning, supported on an iron framework. These cars are very common in the Southern cities and in South America, where the weather always renders riding on the roof pleasant. The new car is to be followed shortly by nine others. As these cars cannot pass under the arch at Vesey street, they are driven to Park place and Broadway.
17 November 1876, New York Daily Graphic, pg. 182:
(Illustration. The vehicle displays "BROADWAY & CANAL ST -- SIXTH AVENUE - ed.)
A NEW PHASE OF THE RAPID-TRANSIT WAR.
THE NEW "DOUBLE-DECK" CAR RECENTLY PUT ON THE SIXTH AVENUE RAILROAD.