I've made sparkling apple cider twice before. I guess it's more like a champagne/wine than a cider, because I think they turned out to be about 11% alcohol or so. I took the pure juice and cut it with just over an equal amount of water. Added sugar, etc and femented. After 3 to 4 weeks and an intermediate racking somewhere along the line, I racked into a secondary containing sugar pre-dissolved in hot water. I used 1/4 cup of sugar per imperial gallon. (I used corn the first time, cane the second time). I bottled in standard 341 ml beer bottles with crown caps. I think I could have cut back a bit on the sugar, since beers call for about 3/4 cup for an entire 5 imp gal batch (or about 3/4ths of a teaspoon per beer bottle), but I've made beers with vastly different amounts of sugar at bottling, and have had no ill effects aside from some beers being a little bit more bubbly. I've yet to lose one to explosion.
I bottled them dry. Haven't tried stabalizing and sweetening. I prefer dry anyway.
I still have a couple bottles from 1996 and 1997. I think they should get opened soon, maybe New Years Eve.