Cassell's Dictionary of Slang gives plenty of cocaine-related uses of "coke" going back to the early 20th century, and for "cokey", the second definition given is "pertaining to cocaine" (1940s+). However the first definition of "cokey" is nothing to do with drugs: it is "foolish, silly" (US, 1930s - 40s).

One of the other meanings given for "coke" (aoart from "cocaine" that is) is "an eccentric, a fool" (1930s), which I guess is probably where "cokey" in this sense comes from.

The same dictionary gives "cokey" used as a noun as an alternative spelling of "cokie" = "a habitual user of heroin or opium" (1910s+) (as Marisaupa said above), but in the song it's clearly an adjective, so my guess is that "foolish, silly" is the most likely meaning here.