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

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.

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.

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.