Assuming you are using apple juice at 1.050 or so, 1/2 cup of juice per two litres should increase the SG by about 0.006 which is roughly 12 g per litre of fermentable sugar (around 2-3 teaspoons), which would probably give you a fairly robust 3.5 volumes of CO2. (I think my math is correct... 0.125 litres of juice at 1.050 plus 2.0 litres at 1.000 = 0.050 divided by 9 half cups. Feel free to correct me if this isn't right)
It depends a bit on how fizzy you want it. Slight or Perlant carbonation is about 1 volume of CO2 and requires about 2 g (about 1/2 teaspoon) per litre of fermentable sugar. "Normal" or Petillant carbonation is around 2 volumes of CO2 and requires anything from 4-8 g (up to 1 to 2 teaspoons) per litre and really fizzy like champagne is anything above 3 volumes. The brewers friend carbonation calculator is quite useful for this sort of thing, as is Jolicoeur table 15.3.
With cider I add the priming juice or sugar at bottling time once it has fully fermented (hopefully at SG 1.000) and increase the SG to the level that I need for carbonation, measuring in the bottling bucket with a hydrometer. Roughly, an increase of 0.001 will give Perlant and 0.002 to 0.004 will give Petillant carbonation, so your possible 1.006 would be a bit more than this.
I have considered trying to bottle at those SG levels before fermentation is complete, but it all seems too hard since it may stall at something above 1.000 (SO4 has done this to me) and taking samples seem to be too much trouble, especially if it hasn't cleared... it is easier to just add sugar or juice, after all we are making something to drink, not attempting rocket surgery!
