The word on the street is Ohlins 25mm kit. At least thats what I have heard. But I don't know for sure because I don't race one.
Do they make a 25mm kit for the Big Piston Fork? I ran the 25 mm kit on my 06 ZX6rr - the difference was night/day.
The problem you have is too much grip on the front tire. I recommend lofting it 2 or 3 inchs off the pavement to cure front end chatter completely.
^ yes, i also heard that they do make the 25 mil kit for the BPF forks. OP, what tires you runnin'? if you're on bridgestone 003's, i know there's a certain compound that gives people lots of chatter so you might try a different tire.
Found the 25 mm kit for the BPF: http://www.ohlins.com/Our-products/Motorcycle/Products/Hypersport/FGK-144/ http://www.ohlins.com/Products/MountingInstructions/MI_FGK144.pdf That's what I'd be doing for sure. Have it installed and setup by someone you trust.
The easiest solution is to put in a FGK (25 mil) kit. Even then, you can get all kinds of chatter with certain tires, but there are solutions. If you want a magic clicker setting or something cheap, you're probably going to strike out. Matt Lynn has an 09 ZX-6R and is reasonably happy with the forks now that we've sorted some of the issues out. One of the best parts about upgrading to the 25 mil kit is that the fork springs are accessible on the top.
I'm on an '08 ZX-10(also notorious for chatter...) and have had some success reducing the chatter by make adjustments to the front tire pressure.
Talking with Matt Myers at Laguna Seca a few weeks ago, he said that the chatter problem has frustrated Elena all year as well. He did say that they have had some decent results recently with some special kit/parts that they've been trying in the forks but they still haven't been able to make the problem(s) go away entirely. Good luck!
So you want the "fix" just typed out here for you? Thats a good one!! Your not going to fix it unless you________________________? If some body fills it in, i want it too cause for 6 months I nor Kawasaki has it cured!!