Right you are, Tom2...
Colt lays claim to the innovation in the history section of their website:
"During the 1880s, Colt produced a full line of weapons ranging in size from concealable derringers to hammerless shotguns. The line encompassed a large number of double action revolvers in various caliber, slide and pump action rifles, and the first revolvers with swing-out cylinders for easier loading."
Edward C. Ezell seems to back this up in Handguns of the World (chapter 2, page 63), detailing work done by Colt designers William Mason (who designed the Lightning DA), Horace Lord, and most importantly Carl J. Ehbets, with with the first of Mason's designs garnering a patent for Colt in 1881. It was Ehbet's design that became the Model 1889.
I think I remember hearing that a French gunmaker had come up with one before that, but the earliest mention I can find of such a revolver in production is the notable French 1892 Ordnance Revolver. A civilian version may have been in production there earlier, but again, I can find no mention of it.