Coppa Mai Tai Cocktail. The Mai Tai is a delicious Tiki cocktail with a special name from the Tahitian. The story goes that Vic Trader (the inventor of many tiki cocktails) first made this cocktail for friends from Tahiti. They replied “Mai Tai” to the cocktail what is Tahitian for “fantastic” or “irresistible”. Tiki cocktails are tropical fruit cocktails with rum and colorful side dishes.