What is the origin of a “coke hand” (a hand of cards holding no aces or cards higher than a nine.?

I have never heard that expression. However it may be very regional. Certain slang is only applicable or understood within an area of a few blocks, or even by a single family. Please refer to the people who use the expression. They may know.

One guess, if someone has such a horrible hand in poker, they may want to use that opportunity to excuse themselves from the table to get a Coke (referring to the beverage Coca-Cola)