Sweet and carbonated is tough. You have to make sure the yeast do not continue to eat the sugars.
If you are kegging, you can stabilize the yeast with campden and sorbate, then add sugar and force carb.
But if you are priming, you need active yeast to turn the priming sugar into bubbles. You have two options. First, you can ferment until try, then backsweeten with an unfermentable sweetener. Then add priming sugar and bottle. The yeast will eat the priming sugar but not the sweetener. Second, you could ferment incompletely. Then bottle while fermentation is still slightly active. Once you reach your desired level of carbonation, pasteurize the bottles in a pressure cooker to kill the yeast. I believe there is a sticky in the Cider forum that talks about this pasteurization method.