Cidersugar - I make beer and get very good carbonation with 3-4 cup sugar per 5 gallons. Since you want lower carbonation that a typical beer try 1-2 cup sugar per 5 gallons. You will still get some carbonation but not a big head like a Pilsner beer. More like a British Ale. The 1-2 cup corn sugar will weigh about 70 grams.
I would just go ahead and use corn or table sugar for the carbonation. But if you want to use juice here's a way to estimate the fermentable extract (sugar?) in juice.
Water weighs about 8.329 lbs-gallon. Calculate the weight of one gallon juice in pounds sp.gr.*8.329 Convert the specific gravity to Brix here's a simple conversion; Brix = (259-sp.gr.)-259*-1 Calculate the weight of extract in juice (weight of 1 gallon juice * Brix)-100 Now you know how many pounds of extract is in a gallon of juice. Convert to grams and you can calculate how many gallons of juice will be needed to provide 70 grams of sugar.
Note: This buttumes all the extract is fermentable. If you are working with clear apple juice this is probably a good extimate.
Bill Frazier Olathe, Kansas USA