I'm sorry in taking so long to reply. I'm not in MN, but I can tell you that my own experience both as a landlord and as a renter is that private landlords are much more willing to overlook things like felony records than the big corporate/property management type places. You may be able to rent a small house further out in the country for the same cost as an apartment in town.
I agree with GingerM. Most landlords use management companies, and you won't have any luck with them. You'd pay a $25 or $35 fee just to be turned down. I had better luck with private landlords, especially if you look for someone renting their basement, or the other half of a duplex. Some of those people will also require a background check, but at least you can talk to them one on one and they may give you a chance.
When I was honest about my background and showed them that I was sincere about being successful out of prison, they gave me a shot. I took their trust seriously, and it motivated me to be worthy of that trust (and keep that door open for the next guy). I made such a good impression on the owner of one small apartment building that he hired me on the side to do some of the maintenance in the building. That included trusting me to go into other apartments.
There is hope. I don't have a list of landlords, but I would recommend checking Craigslist and local rental listings for someone looking to rent a duplex, a basement or even a room in their house, etc. I always started the conversation by asking if the property was managed privately, or by a management company. Saved a lot of time.