It may be best for you to rent directly from a home owner, they'll likely listen a bit more to your circumstances. Property management companies usually have strict guidelines. Take a look at craigslist, but be careful, if the price is too good to be true then it could be a scam. I have had people call me regarding certain houses only to find they are actually bank owned homes that someone is trying to "rent" ... they'll take your deposit and disappear.
You may also look at the local greensheet, there is often homes for rent by owners in those.
Always Glad to Help,
Ryan Mihld - Broker
Home Buyers Realty Group, Inc.