Start off diluting it slightly and then work your way down, if juice is the only thing that will work. If you do it gradually, she may not notice. We are not doing juice now, but when we did it was limited to 1 or 2 cups a day - otherwise my kids would drink juice all day and never eat anything. I knew one kid who actually did that and she didn't grow for a year until her mom was sent to a dietitian to review her diet.
If you are ok with artificial sweeteners there are lots of drinks. I find artificial sweeteners sorta gross, so I don't know much about good choices there, sorry.