Depending on the other elements of the dish (natch) I would first look at herbs.
Mint is a logical dessert flavour (maybe too much so). If you can get your hands on some fresh Holy Basil that would be a winner. It has an almost tropical fruit quality.
Either way green herbs can easily be blended into something like an angaise. Or just sheared into a syrup, hit with some agar agar and made into a fluid gel.
Think about green beverages (Chartreuse?) that can be turned into a sauce.
Heck, its a Christmas thing, right? A puree of those green "fruit cake" cherries might do the trick, and be seasonally applicable!
Al