You'll need to go late winter or early spring before the green up while the grass is short. There are some places where you can see herds of them on top of the marsh and running like miniature buffalo. Unfortunately most places were nutria populations are still high are on private land owned by large companies (Miami Corp, Vermillion Corp, Continental Land and Fur) who already lease it out to duck hunters, commercial fisherman, and trappers.
Most nutrias that are killed for the Coast Wide Nutria Program (CNCP) are done so on private land simply by riding around and shooting them from an air boat. This method would be illegal on public land. Probably 90% of the tails are collected by 10% of the trappers. Check out
www.nutria.com for some resources that might be helpful. If you want to contact a Louisiana Wildlife and Fishers Office I'd suggest contacting the New Iberia office. That is the office where people that do the nutria damage surveys work out of. Maybe someone there can point you in a good direction.
If you get kill some there is a LOT of meat on them and it's delicious.