The carbine will appear in Sterling's inventory only after you got his ammo supply.
It took me forever to play that trick with Chief Hanlon to get ahold of his Ranger Sequoia...
Spoiler
Sterling plays a role in Raul's personal little quest, so killing him before completing that
will turn that quest impossible to finish.
Also, be aware that Sterling and all of 1st Recon will head to Camp Forlorn Hope once
you complete the quest that requires killing the Fiends leaders, and once there getting the La Longue Carabine will be neigh to impossible
as they all stand close together in a circle and thus you have no chances of being [HIDDEN] and succeed in pickpocketing.
Being unencumbered, light or no armor at all, Sneak skill in the 35-50 range helps alot when pickpocketing. Also, try to stand in the darkest corner possible,
and please... Turn off that Pip-Boy light.
I have the feeling that a Stealth boy goes 'on top' of your natural sneakyness,
since back at the time my Sneak skill wasn't that high, I was getting caught alot even when I would activate one.