How can I get La Longue Carabine from Corporal Sterling in Fallout NV?

Solution 1:

An alternative to killing him is to pickpocket the ammo he carries, then fast travel and come back.

When you return he will have the gun in his inventory available to be stolen.

Solution 2:

If you don't want to kill him but don't care about losing a slight bit of rep with NCR, you can try and shoot the gun out of his hands then pick it up. If you do this and travel away from the airport (or Camp Hope, depends on where he got sent) and wait three in-game days, they've forgotten you and everything is back to normal.

Solution 3:

No Negative Karma. No significant NCR loss. Sterling still alive. Clean digital conscience!

Wait until he is sleeping.
Talk to him. This will allow you some time to get away from him before he talks to you, lead him to the front gate because he will not stop following until he says howdy.
Wait until he turns around after the conversation, sneak, (stealth boy almost certainly necessary) -SAVE-
Sneak Critical his weapon. (May take some tries)
He'll draw. Shoot the weapon from his hands. (A few tries here too, may be wise to save again after landing the sneak critical on his weapon with a 4570. After which you should be able to holster your weapon and he should put his down as well. Orris in Freeside has a hunting revolver. You must disarm Sterling while he is holding weapon or it seems to disappear.) After shooting the weapon from his hands he will follow you out of Camp McCarran, and the ends of the earth.
Grab it.
Exit.
He'll follow, but the entire NCR won't be shooting at you, and you can outdistance him pretty quickly if you holster you weapon, allowing you to fast travel to a repair shop. Because it will be broken.

Solution 4:

I found the easiest way to get it without losing reputation, karma, or even being noticed is to wait until he sleeps in the tent to kill him.

Two of the beds have a point in the corner that you can easily get into. Once you're in there, sneak and use a stealth boy and use a melee weapon on his head (not for extra damage just because it is the point that is closest to you).
I found that it works most reliably with the sword you get by killing Davison in the Reppcon test facility basement, so you can get it during the quest with Manny and the bright brotherhood.

I found this to be a better way of getting the gun than stealing the ammo because at least on Xbox when you pickpocket the ammo from him it just won't give you the ammo, and I'm guessing this just happens if you get caught pickpocketing by anyone.
Thus you can't use that method so the only way to get it is by killing him or finding some way for him to die naturally like by an enemy.

Solution 5:

The only way to get the rifle is by killing Corporal Sterling and looting his corpse.

The best ways to do this without angering the NCR is to use the "Sandman" perk, or get a silenced sniper rifle and shoot him in the head from a position where you can not be seen.