Your tin roof is sweating on the inside right?
You need more ventilation.
A vapor barrier on the bare metal (inside) will also help - I put styrofoam insulation against the metal inside my coop - this helps keep it from sweating, but plenty of ventilation along the roof line important too.
Can you post some photos of the inside of your coop - ceiling, ventilation, etc.?
What type of roofing material is on the coop - metal?
Where do you live - country/state?