I supposed It depends on what you're going to do there and where you are going to be. If you are going to be working with an organization, they can probably help you find one if they don't already provide it.
If you are not, and you really need to find something on your own, I am also interested in any information, as I am not yet sure what my situation will be, whether I'll be working with an Organization or not.
I can tell you this. I have friends in Haiti, both Haitian and expats, and this is what I have picked up in bits and pieces from them. Most Haitians pay their rent by the year instead of by the month, and it can be as little as $700/year (maybe even less?) However, things are different for an expat, especially if you are caucasian. Because we have added risk of kidnapping, robbery or other things, it is important to live in a secure enough location. These places can be very nice with security, running water, electricity, internet and other things that are luxuries in Haiti. However, rent for a place like this in Port-au-Prince can be rival rents in major cities in America and Europe. From what I can understand, there aren't many options that are in between these two, but if someone wants to correct me I'd be happy to be wrong.