How much are you willing to spend? Would you like something that's semi-permanent or do you just want space heaters?

One solution is to install a vented kerosene furnace (I heat my house with a pair of them) such as those sold under the Toyostove brand (http://www.toyotomiusa.com/). That eliminates the moisture problem entirely, as the air intake and exhaust are both external. I've seen kero furnaces on Craigslist cheap, as many people are converting to natural gas. Installation is easy, as long as you have a window or a wall that can be drilled for the flue pipe.

You may also see Monitor kero furnaces, but given the choice, I would go with Toyo. I have one of each and the monitor requires burner rebuilds every 2-3 years, whereas the Toyo has required nothing in the 10 years or so that I've owned it. Monitors also have a less than stellar reputation for reliability, though I haven't had any such issues with mine.

If your house has natural gas, you can get a similar vented gas furnace (Rinnai makes them). There are also propane versions available, which are commonly used in mobile homes.