SLANGERUP, Denmark—For more than a century, businesses have struggled to solve a curiously complicated challenge: How to make a paper bottle that doesn’t get soggy and keeps drinks fresh.

Diageo, the manufacturer of Don Julio Tequila and Smirnoff Vodka, has launched the on-trade trial of a 90% paper-based bottle for Johnnie Walker Black Label. Starting today (25 September), the ...