Backsweeten kegged cider - after carbing?

How would I go about backsweetening hard cider after it's carbed up, in a keg?

I've got a batch of pomegranate cherry apple cider in a keg in my fridge, happily carbing up. It tasted pretty nice, but a tad dry, when I racked into the keg a couple weeks ago. But certainly fine for what we like around the house.

Now, having sampled a bit, I can taste an off flavor I've tasted before: the vinegary sort of flavor. So something's going on in there that I didn't want, and I've had it once before from the same type of juice, so I know where this winds up: needing to sweeten to make it drinkable.

I'd ideally like to not waste the carb that's in there already, can I boil up some sugar or add some apple juice concentrate or something directly to the keg, purge it a few times to get rid of oxygen and then shake the crap out of it to mix?

It finished around 1.000 but I'd like to bring it up to around 1.010 or so I think. Bit shy of 5 gallons. Any advice on how much sugar or juice to use would be cool, just looking to salvage it and make it more drinkable.

And yes I know it'll re-ferment if I warm it up, that's not going to happen, it's staying in the fridge or kegerator until it's done

Come on now, don't make me serve this vinegary stuff to guests, I swear I'll do it!

really, vinegary?? or just tart? cuz if it's vinegar, i would only serve it to a salad. you can easily enough calculate how much sugar to add to get it to 1.010, but in my experience you have to taste along the way to get the right sweetness. there is no problem at all to adding sugar after you carb, exactly as you suggested, and indeed only add liquid since dry sugar will go geyseral and you'll be lionel ritchie; dancing on the ceiling. with a mop.
here's my early morning math; i use % (=brix) since it's easy to calculate and convert to/from gravity.
1.010 means 2.56% sugar, = 2.56 g per 100 ml, or 25.6 grams per liter. simple as that, multiply your number of liters by 25.6. bit shy of 5 gallons (us?) = 17 L, so you want 435 g sugar. personally i would use juice or concentrate if possible so work out how much sugar is in your concentrate and add ~435 of that. an older post on here said that a can of concentrate contains 174g sugar. no idea if that's true but if so there you go, 2.5 cans and you're at 1.010, neglecting the small change in overall volume, bigger change in volume if you use juice but it's probably close enough.

Right on, thanks for that. Yep it's a slight bit vinegary, more than tart. We only have dry ciders here because that's our usual style we like to drink, but this one is way off suddenly. So sad...

Well I wound up getting scared of 435g of corn sugar being added (I also got lazy and opted against the canned juice idea, but it would probably have worked out nice). I boiled up 300g of corn sugar in 2 cups of water, cooled it down, purged and popped the keg of cider and added that in. Nice and easy, didn't fizz much at all even though it was warmer than the cider.

Purged 3 times and shook it all up for a bit shy of a minute. Back on gas, and it tastes a lot better now, whew! Not as sweet as I was shooting for but certainly drinkable. 430g would probably have been right on the money, Dinnerstick. Good maths there!

For future reference I find that 2-3 cans of frozen apple juice concentrate adds a nice apple flavor and will take a dry cider to semi sweet. It mixes nicely also. That Dinnerstick fella is pretty sharp......must be the Dutch blood......Disclaimer: My maternal Grandmother was 100% Dutch.