It's no surprise that there's no information online about a business seemingly as old as the "West Side Variety Shop," but that there's next to nothing about a featured product like Polo Club — is a puzzlement.
I did stumble upon one mention in a 1939 edition of the Manlius, New York Thrift-News, where a grocer called the Red & White touted 28-oz. Polos at four for a quarter, Thursday, Friday, and Saturday. Look for that notice below the ad promoting Sweeney's Poison Wheat.
Surviving painted ad for Polo Club Quality Beverages
Stillwater Ave., Stamford, Connecticut