Juice recipe recommendation engine to give me recipes based on the ingredients I already have?
Search engines like that, as you know, are more complicated to build than the standard recipe searches you see in most places, and many websites that have food recipes and are heavily utilized don't have them.
If you want to ultimately be able to make juice based on the ingredients on hand, what I'd recommend is becoming more proficient at matching flavor profiles and knowing what the essentials of juice are.  You can learn more about possible good flavor pairings at this website (more info about the website's technique for pairing flavors).  You can also learn a ton at khymos.org or from The Flavor Bible by Page and Dornenburg.  For learning ratios, start with simple recipes such as these or even try and break down your ideal juice by sugar and water components and then look at how much sweetness and water are in each possible ingredient.
If you get stuck on a particular recipe, you can always ask how to improve it here.