I've wondered about carbing with dry ice before.
So many milligrams of dry ice do you need to add to a 12 oz bottle of cider to carbonate it to 2.0 volumes?
The amount would be very small. Per google, 1lb dry ice = 8.3 cf of co2. 5 gal is .67 cf. To carb a keg at 2 volumes, about 2.7 oz of dry ice would be needed. A 12oz bottle would need 1.5 grams.
That small of an amount would be a PIA to measure. If you have ever bought dry ice by the pound, you surely have watched the checker try to weigh the block while it continues to get lighter causing the computer to think the scale isn't steady.