Pole barn problem.....

[quicksandfarmer]

You have to figure out how the moisture is getting in. It could be rain coming in through the roof, side or floor. It could be groundwater coming through the floor. It could be coming out of the building as the lumber dries (pressure treated holds a lot of water). It could be from the sweat and breath of the inhabitants. It could be warm humid air that comes in during the day and gets trapped.

Once moisture gets in a building it doesn't get out, you get your own water cycle where during the day the building heats in the sun and the water evaporates and rises, in the evening it cools against the roof and rains inside. It's very destructive.

If the water is coming in as rainwater or groundwater, you need to keep it out. You need to exclude this as a possibility before trying anything else. Moisture can come through a concrete slab that is not visibly wet. A standard test is to put a sheet of plastic over your concrete floor and see if water condenses between the plastic and the floor. If it does, you have an infiltration problem.

If there isn't an infiltration problem, the water is in the air. There's two ways to get rid of it: replace it with drier air through ventilation or remove the moisture directly with a dehumidifier. If the space isn't heated ventilation is cheaper, you should be able to do it for free.

Ventilation doesn't always work: if the outside dew point is higher than the inside dew point, ventilation just makes it worse. That is often the case here in the summer, my preference in the summer is to have buildings either wide open or sealed shut with a dehumidifier.

 

[dave1949]

I think you need to consider it as two separate issues that are divided by the ceiling/rafter insulation.

1) Ventilating the air space above the rafters. A gable fan at each end might do fine for that. The type without shutters and a thermostat will run when hot, and allow air flow end-to-end even when not running. These should also reduce the heat load in summer.

2) Controlling the humidity below the rafters.
I agree with quicksandfarmer's comment:
Once moisture gets in a building it doesn't get out, you get your own water cycle where during the day the building heats in the sun and the water evaporates and rises, in the evening it cools against the roof and rains inside. It's very destructive.

Most of the time, some air exchange will be your friend because it removes the build-up of accumulating moisture. This is exactly what occurs in my house if I don't get enough air through it in winter. No ceiling rain , but plenty of window condensation at night.

There are fairly inexpensive wall-mounted ventilation/exhaust fans that will move a lot of air out, given some has a place to come in. With no windows, you will have to open it up somewhere across the building from the exhaust fan. You could use exhaust fan vents of the type with flaps that the air pushes open, pulls open in your case. You could use a backdraft damper that the negative air pressure of the exhaust fan will pull open, they shut with gravity.