The New Mexico military base oryx hunt is a tag you apply for and is $1500 I think. A Texas oryx is an over the counter liscense but they are usually more money.
The draw hunts on the missle range are 1 day only hunts due to higher security now days. there is also a depredation hunt off range that is open year round, however this is also a draw hunt ( I drew this tag this year) In my opinion for a non-res the depredation " hunt" may be better as you can spend more time out here. You will get one on the range hunt in one day, but that's alot of miles to travel for a one day hunt.Some land owners sell permits but I have no idea what they get.