I have that problem exactly....
The previous owner covered the Airstream with a tarp because the 2 roof vents leaked. The results are exactly as you describe, plus there are some brown marks that we can't figure out. ?Maybe tree sap/"acid" rain marks?. Both the brown and black marks are only where the clear coat had come off.
I attended the 4 Corner Unit Restoration Rally in June here in ABQ to learn how to fix these marks. Levon, the polishing expert, tried a few things. We found that using Nuvite S (non-cutting) worked pretty well on the marks. I have purchased Removall to strip the whole trailer, and have some S to work on the marks. Levon said the trailer would polish up beautifully, but I'm not ready to take that on yet.
I've attached some pictures to show the exterior state of my Airstream. Once it cools off in ABQ, I thought I'd work on the exterior. By the way, the Restoration Rally was great!