Can the business across the street ban liquor from its grounds even next to the street?

[bibleguy]

The business across the street has had problems with people drinking to excess and collapsing in front of their parking lot. The neighborhood drunkards gather under the trees on their grounds adjacent to the street and drink themselves into a stupor requiring ambulance services.
The shops (which don't sell liquor) want to put up signs prohibiting the use of alcohol on their grounds.