Time.  When I added the sand to my coop and run it also seemed like it would NEVER dry.  I put my chooks in even though it was wet and they didn't have any troubles with the humidity.  I have a LOT of ventilation/crossbreeze so I knew that would wick the moist air away quickly.  After about four to five weeks, the coop finally dried.  You want to know the truly humorous thing?  I actually miss that lightly-moist sand now.  It can get sooooo dry and dusty in the coop that I actually HAVE to lightly spray water in the coop weekly just to keep dust to a minimum.  
Chickens, through the natural course of chickening, will turn over the sand and help to dry it as they dig/bathe/scratch/flap their wings.  As long as you have great ventilation in your coop, a secure run of adequate size or better yet, access to pasture for your chooks, you'll do fine adding your chooks to sand that isn't completely dry.  Soon you'll likely discover for yourself that weekly spritzing of the coop sand will be in order.