Kur-o-pat-wa has 4 syllables.
Spelled phonetically its:
cur (like the first syllable in "curtain")
oh (as in "Oh my gosh!")
pat (like the diminutive form of "Patrick" or "Patricia")
wa (as in the first half of the word "what")
Here is the Odeo audio
... and here it is as an mp3 file:
For the record, the name is of Polish origin. In Polish the "w" would have a "v" sound. I don't speak Polish. In English "Kuropatwa" means Partridge so you might say we're the Partridge Family. Unfortunately (or fortunately) none of us were ever on that show. ;-) And finally, if you're interested in an English/Polish translation tool, you can find one here.