This image is from the June 1959 issue of Esquire magazine. It says:
“The fabulous mixologist Mariano Licudine of the famed Mai-Kai Restaurant in Florida creates new ways with rum in his Derby Daiquiri. The secret: one ounce of fresh orange juice, one half ounce of fresh lime juice, one scant teaspoon of sugar, one andone half ounces of Puerto Rican white label rum, one cup of crushed ice; mix in a blender for 10 seconds or shake vigorously. The bee? Oh, he’s just buzzy. But this, designated the oficial drink of the Florida Derby, is the DERBY DAIQUIRI.”
This date seems to have confused people into thinking this was named the official drink of the Derby in 1959. The Derby Daiquiri has been on the Mai-Kai drink menu since the earliest printings. And it has always been pictured served in the special Jockey glass. So, I would assume it has been the drink of the Derby since 1957 at least, which is the copyright date on the oldest menus I have seen.
Here is Mai-Kai owner Bob Thornton holding the drink with the original coaster.
Here is my glass with the coaster.
UPDATE 8/10/2011: After extensive research, though the Derby Daiquiri was on the first Mai-Kai menu, it did not become the official drink of the Gulfstream Derby until probably 1959.