You better check to make sure you can hunt them on a refuge. Sherburne NWR, and just about every other refuge I have been to in a couple of different states is closed to coyote and fox hunting. These are all national refuges. I don't know what the Lousville unit is classified as.
You can use rifles on any WMA's, state forests, WPA's (must us NON-Toxic shot shells on any federal WPA's.), Tax Forfeit lands (unless there's a local ordinace against rifles.), county lands. ect... If rifles for coyote hunting are banned on any public ground I don't know about it. As far as Non-Tox shot Dead Coyote by Hevi-Shot is the deal. Expensive, but it's not like you are shooting cases of it, and it kills them DEAD. I used steel up until last year and now would never go back. I havn't shot too many with the scattergun this year but did kill a few called in w/ lights and a few in the yard.
I have the luxury of having some massive tracts of public lands in my hunting areas. I have good luck both running K9 traps before deer season and calling and snaring after deer season. That said, if you're in the south or west metro you should probably invest in a few nearby county plat books and start knocking on some doors. All the land I hunt in the south metro and most of southern MN, aside from the SE and the SW corners, is private.
You can also get WMA maps from the info desk at the DNR. Either stop in or call. They used to be free and came in two parts: North and South.
If you do hunt public land it will pay you to NOT park where everyone else does and NOT enter from the areas everyone else does even if this means you have to walk farther. When you hunt pressured land you have to have a perfect set-up to consistently kill coyotes.
Good luck,
Tim