As Martijn correctly stated, experience with Smalltalk will help, as will experience with LOGO, or Lisp, or *any* other declarative language - including SQL.
It also helps to remember that the core paradigm shift here is imperative -> declarative. OO is completely orthogonal to this, and you can write object-oriented code in both imperative and declarative styles.
Draw on every bit of experience you have in working with immutability. For most Java devs this is going to be SQL and JodaTime, you might also have some experience with Hadoop or NoSQL databases that can help here.
Top Tip: Most established Scala devs will view the difference between declarative/imperative in the same way as Java devs view the difference between JodaTime and Java's Date/Calendar types. The imperative way used in Java is risky; You're dealing with values that can be changed in another thread even as you're working on them, or simply because you passed them as an argument to another method - just try using an instance of SimpleDateParser across multiple threads to see a terrifying and eye-opening example of this in action. Use your experience of JodaTime, it'll help you out a lot here.
Finally, draw on mathematics and real-world intuition about how things work. If you pass `christmas` as an argument to some function, you still expect it to still be December 25th when that function returns. At it's heart, Functional Programming is applying this same core expectation to every value that you pass to every function in your program. You should work wherever possible with pure functions (don't mutate their arguments, don't mutate any state external to the function, and always return the same output given the same inputs). An "FP Language" is just a language with constructs and syntax that make it easier to program in this style; there's nothing to stop you writing a functional program in C or Java, if you so wish.
Finally... Just keep at it. You'll reach a point where recursion (and tail recursion) just "clicks" and begins to make perfect sense. And remember that with coursera you're not *just* learning FP; you're also learning algebraic data types, pattern matching, and working with a more powerful type system. These are all concepts that work very well alongside FP, but aren't essential to the paradigm.