It's all in the ingredients?
hi Julian, it's a bit hard to explain so I'll try to draw an analogy. Let's say you consider yourself to be a pretty darn good cook. You make a mean tuna casserole.
Then one day on vacation on the other side of the world, you go to a fancy restaurant and have the most incredible meal. You insist on speaking to the chef, who's too busy, but your waiter is happy to tell you what is in each dish. So he tells you in broken english, because it's not his first langauge. But you get the 'gist' of it, or at least the basic ingredients...
You can't wait to recreate this awesome meal when you get home.
Now, let's say the meal calls for Kobe beef (Vinnie C.) but all they have at Giant is farm raised Montana... The chef marinates his beef in spices unavailable to you (Eventide, Neve)... oh, and you are not a world-renowned chef who's been cooking since age 7 (Hugh Padgham).
Get my point?
Vinnie Coliauta is a virtuoso. Sting is a genius, and Sting was probably leaning over the shoulder of his world-renowned sound engineers and producers while pro drum techs came into a professionally designed room to tune Vinnie's drums and set up about thirty thousand dollars worth of mikes.
After the perfect take, a team of experts huddle in a control room that rivals the Space Shuttle, and spend a few weeks getting the perfect blend of compression, reverb, stereo balance, etc. etc...

So, now that I got that out of my system...
My point is even if you have the right "equipment" you probably won't get that "sound". I bet if Vinnie C. himself tried to recreate what he did for Sting over ten years ago, he probably could MAYBE come close.
Now, do you know how to tune drums? Most drummers I know can't. If not, I say start there. Most drummers don't even know how to properly hit a drum... not saying you can't... just pointing out a fact. I'm a drummer so I can say that.
But in the interest of helping a fellow drummer, I would suggest looking into the specs of Vinnie's kit back then. I know he liked to play Yamaha but he might've used an old Gretsch kit for those sessions. Find out what heads he was using. What woods. What size and depth. Then try to recreate the pitch. Google, baby, google. Oh, and
http://www.drummerworld.com
