Swift
First, mixing tires is bad. I know drifters IRL do it. But in the GAME there is no need. Just put N2 or N1 all the way around.
All of the S2000's are driftable. Thought the non-tuner versions are a bit easier. It's about how they are setup. In there original setup they are set to stick to the road like glue. So you need to tweak out the spring rates, camber, toe and stabilizers to allow for more grip up front and easier weight shifting. This is probably what's giving you so much trouble right now.
TankSpanker, can you give some suggestions on settings. I'd appreciate it!
what, me?

I think breaker is the guy you want - he's done some good drifting in some S2000's
lemme just fire up my game - i had an S2000 i was working on a week or so ago
[reserved for settings suggestions]
ok, fired up the game
i had a stock '01 Honda S2000 Type V on N2's and was drifting it on autumn ring mini reverse with relative ease.....didnt want to fishtail too much or anything. quite stable. It did require a decent amount of weight shifting though.
259hp
no weight reductions
nothing but N2's and an oil change
(i bought it with 10km on the clock, so a chassis refresh may be needed for others)
oh, and its red
anyways, i bought racing suspension to see if I could make it more slide-happy
ok, did 12 quick laps or so and found the drifting to be improved slightly by the following changes to the suspension:
springs: 6.4 | 5.8 (no change from when racing suspension is equipped)
ride height: 95mm | 95mm
shock bound: 4 | 4
shock rebound: 8 | 4
camber: 2.5 | 0.8
toe angle: 0 | -1
stabilizers: 4 | 2
the front shock bound can be raised slightly without penalty, i have it set as low as i do because you can attack the curbs harder with it. The car jumped around on me a little bit more on the small course when it was higher.
in this state the car is quite happy to drift by lift off and feinting techniques (and yes, the ebrake still works too). Braking drift is less effective, but i attribute that to the lack of racing brakes and a balance controller. Power over is possible through some of the tighter corners on the course, but more power would likely be required for a larger course with wider turns.