Okay let me ask you you have any windows in your basement that is big enough to allow small AC?.
You know a dehumidifier has the same mechanics of an AC with a bit of modifications to have the condensation of the coilsto drip into a container. In one of my houses I put in a small AC in a basement window and where it dripped out I put a plastic sheet.Making sure it is graded away to go three or 4 feet away from the foundation which should stop water from trying to come in. One could put washed stone over or even bark mulch to make it look better. The benefit of this to is it would contribute to the cooling of your basement in hot weather.
Now they also sell portable ACs. These are on wheels and come with a vent that you can put into a window. You can buy them that have the advantage of not having to empty the water tank. I have one that we use for backup that also blows the condensed water with the hot air out of that same tube..
What I don't like about those portable air conditioners is the fact that they are blowing air out, and therefore somewhere in your house that same amount of hot humid air is coming in. Yes it helps cool your room or part of the house, but is not as efficient of one's that don't do that, i.e. like the common window rattlers.