ive looked into it before.
right now there is a bounty on nutria($5). and only land holders can cash in.
i talked to several places that were complaining of levee damage by the nutrias, ALL wanted me to pay to help them out. one even wanted $750py to ONLY hunt nutria.
if you want to go on a hunt, forget private land/leases, talk to a game warden/ranger about wildlife preserves/state land.
they will know where the nutrias live in their regions, and may be able to recommend somebody to take you out.
or you could try the army corp. of engineers, they are always fighting the nutrias that tunnel the levees. you can get a special permit to shoot them on c.o.e. land, but may be restricted on choice of cartridge.
i ended up just giving up as i decided it wasn't worth the hassle just to kill some soggy rats.