You can't.
If you stabilise and back sweeten that way, the only way to carbonate it is to force carbonate in a keg and then bottle it. If you are new to this, you mightn't have the equipment to do that, though.
Alternatively, if you ferment it out, add sugar to back sweeten and the yeasties are still functional, they will chew up your backsweetening sugar, giving you a dry cider (and possible exploding bottles if they are over-carbonated). You can try to stop them by putting your bottles in the fridge once it is the correct amount of carbonation vs sweetness, but that will really only slow them down and eventually you will have the same problem (unless you drink it quickly).
The last option is to use a nonfermentable sugar to backsweeten, like lactose or an artificial sweetener, but for these it depends on your tastebuds and whether you want to use them (for example, I tried lactose and hate it in cider or ginger beer. Others are ok with it)