"Reiko" means cold coffee = iced coffee. The exact origin is unknown, but it seems that it may have spread from the abbreviation used by the staff when taking orders at a coffee shop.
Osaka has the highest number of coffee shops in Japan, and because they are all close together, the staff and regular customers are familiar to each other, and the word was born out of this sense of closeness. The name seems to reflect the closeness of human relationships unique to Osaka.