The drinks should appear in the cooler in less than 30 seconds. Make sure you have enough berries:

Tintoberry Splash: 100 tintoberries
Amarberry Fizz: 100 amarberries
Azulberry Blast: 100 azulberries
Tintamar Spritz: 50 tintoberries, 50 amarberries
Azulamar Quench: 50 azulberries, 50 amarberries
Mejoberry Sipper: 100 mejoberries
Narcoberry Snooze: 100 narcoberries
Stimberry Jolt: 100 stimberries

I think it may be the stacking mod I am using: StackMeMore v1.08. The cooler does not produce any drinks no matter how many or which berries I provide. It also changes the sparkpowder though the cooloer glows when provided sparkpowder and activated.

I tested it on 2 servers running pegi's resource stacks and on local server with no stacks as well as in no-stacks single player It produced the drinks there.
Your stacking mod is the only thing that I can think of that could prevent it from working. maybe it doesn't see the berries in that stacking mod as valid resources. The odd thing is that the cooler allowed the berries, as it only allows valid resources in its inventory (berries and sparkpowder)
I'll see if I can find any more info on it.

Anything more on this issue?..I am using the same stacking mod and having the same issue. Would love to use the mod if it can be compatible with StackMeMore. Thanks for all your work.