Pretty sure that all S2000s are on coilovers, are they not?
A lot of it is to do with the geo of the cars, as well as the suspension setup. The later cars also moved to decent rubber, as well as bigger and heavier wheels. They're not a particularly snappy or bad-handling car, but much like the CGT you have to know what you're doing with regards to setup to get the most out of them.
The OEM dampers and springs are non adjustable man.
Mine was on Bilstiens and I had a FRSU done, then tweaked to suit me by Tom at TGM.
I also had the better OEM S2 17's that improved things loads.
It was set up pretty well man but I don't profess to be a driving master, I know what's what's but that's only 10% of being able to do it.
I had it round Castle Coombe in day and it was proper on song that day on that circuit, that and a few certain laps of the Ring are my fondest memories of that car.