You are apparently experiencing condensation. To solve it, you need to realize why it happens. Warm, humid air comes in contact with a surface with a temperature at or below the airs dewpoint. The air cools & can no longer carry it's moisture, the result is condensation.
Crawlspaces are condensation problem areas because the ground keeps them cooler than the outside air. Yours is complicated by the AC ducts, another cool surface. The usual suggested remedy is "Vent the crawlspace". But buy venting it, your letting warm humid air in, thereby creating more condensation.
The best solution is to prevent the moisture from entering the crawlspace. Your partially on your way to solving the problem in that you have a ground vapor barrier. This prevents most ground moisture from entering. The next step is to prevent outside air moisture from entering. To accomplish this seal shut your vents, the more airtight the better. I would also suggest insulating the perimeter foundation walls, perhaps styrofoam on the inside crawlspace walls. The next step is to include the crawlspace in your indorr air circulation ( the previous steps have included your crawlspace in you thermal envelope which means that this space should be treated like the rest of you house. Talk to your HVAC contractor about this. This will especially be useful, since AC removes moisture from he air. In cool weather, you would include it in your heating system, giving you the benefit of warmer floors.)
Although I've used & recommended this approach in colder climates, the physics is the same & should work well.