If there's still a couple gravity points to move, I'd put it in there uncarbonated, hit it with 15 or so PSI of pressure to seal up the keg and let it naturally carb in the keg. I've done this before. Once it's done, you can either transfer to a new keg through the liquid tubes (which is what I would typically do), or if the keg is going to remain still/unagitated, you'd probably be fine just serving right from the same keg ... first glass may be a little murky, but should be fine after - especially since it's a stout I doubt you're too concerned about clarity of the beer