The "Java of FP" could be C# or F# (although Microsoft isn't willing to go multi-platform, so that might stop it becoming "successful", by many definitions).
But honestly, I don't think there is a powerful enough vector available to carry FP. C had Unix. Java had the net. A novel way to think about the next "Java of FP" is to think of what vector could matter, and then what FP language is well-placed to be carried by it.
Mobile phones are all I can think of at the moment, but no FP has come of it; the netbooks (which are becoming phones) are plain ol' PCs; and the iPhone runs Objective-C (doesn't it?). What's the next IT revolution?
Actually, time_management is right: the next IT revolution is clearly multi-core.
EDIT: I keep hearing about Intel's CUDA for multicore on GPU's, but it's pretty much the anti-FP, being "recursion free" http://en.wikipedia.org/wiki/CUDA#Limitations