Covering the crawl space with concrete is not really an answer. For one thing, as long as there is adequate ventilation under the house through the crawl space, moisture is not much of a problem. I have seen creeks running under homes. Obviously you don't want any ducts, fixtures or sill plates to get wet, but if the water is confined to the crawl space stemwalls, there is not much damage going on.
Big Bobs suggesion is valid. It would involve digging a ditch along the interior foundation wall with the objective of collecting it at the lowest point and using a drain or sump pump to remove it. IF the problem is just seasonal and not affecting the living space in any way, I would just leave it alone. It is just too hard to work in most crawl spaces. If the moisture buildup results in mold, mildew or threatens the wood components or ducts, then you may need to deal with it. Under no circumstance would it be worthwhile to pave with concrete; however plastic with gravel over it is a good barrier.