I think Verbatim or Sony may have been the first to introduce them. I have a box of Verbatim DS/DD disks with a copyright date of 1988 with diskettes in five colors (orange, red, blue, green, and yellow). I also have a red Sony DS/DD diskette (no box) from around the same time period, at least based on design compared to other Sony diskettes around the same age.
Most of the major disk companies made colored disks in those five colors. I know Maxell, Memorex, and 3M (later Imation) had them. Even some of the generic/store brand disks (i.e. Office Depot) came in colors. I've never seen a colored BASF diskette (unless you count blue DS/DD diskettes, which were pretty common). Maxell also made colored 5.25" floppies, and I think a few other companies did as well. Fuji made colored disks but only in red, green, and blue. I also have a generic, unmarked DS/DD diskette in pale pink of unknown origin.
Imation later made a line of translucent disks to match the iMac (which, of course, had no floppy drive). They came in red, blue, green, orange, and clear. These are pretty cool; I bought a pack alongside my Clamshell to match it (I already had a SuperDisk drive I had won for placing third in a grand opening raffle at an Apple Specialist a few months before I bought the machine).