Options for a small, single room AC with no windows, no drainage possibilities, and not water vapor based
Congratulations - you have eliminated all the ways this might actually work. 

Either deal with it being hotter, or add a few options that you say are "not an option" with the most logical one being a connection to the central A/C. 

With a bucket, you could go with 50 pounds of ice, a fan blowing over it and a bucket for it to drain into as it melts. That will get you 7,200, perhaps 8,200 BTUs before you need to get another 50 lbs of ice...or the equivalent of about an hour's run time for a medium window A/C. Not very practical without a large supply of ice and labor to carry ice and buckets of water.