Tramlining is a not uncommon phenomenon with the combination of wide tyres (especially with the more rigid sidewalls of runflats) and a relatively light vehicle.
Fitting non-RFTs (with the obligatory tyreweld etc.. in the boot) will make a big difference. You may have had sport suspension spec'd which will make a bit more of a difference but someone above has kindly pointed out how you can check this.
Couple of other things worth considering...if you are new to convertibles and sports cars generally, it may just be that you need to acclimatise to the new ride. The Zed is one of the least susceptible convertibles to the phenomenon of scuttle shake (effectively where the front and back of the car flex slightly relative to each other, because of the lack of a roof tying the two together) - it is well braced to pretty much minimise this problem, especially on normal roads.
Its also worth getting your rear springs checked...they are prone to breaking on this vehicle, its a very common problem indeed as you'll see whan browsing the forum, and it will make the ride a bit crashier while still driving normally, so if it has happened, even the previous owner may not have known. Not hugely expensive to replace...more costly if you have all four done - some people recommend Eibachs which lower the suspension a bit, but if you are already unhappy about the ride I'd recommend just using OEM springs...its only the rears that break as far as I know and they are a doddle for a garage to fit.
Lastly, I'll be a bit contentious, because the 'go-faster' boys will be up in arms...the less rubber you have on your rims, the harder the ride....indeed at the extremes (19" or 20" rims) broken alloys are not uncommon. The 2.0 was originally spec'd with 16" rims so before you go to the expense of changing to RFTs, only to find that still doesn't quite do the job, think about fitting 16s. The tyres are also a bit cheaper. Sets often come up on ebay and go for a song.
I bought my four-pot new six years ago because I love ragtop motoring, not because I wanted to drive at 150mph with the roof down. I run very happily on 16s with non-RFTs and the ride, even on our bumpy welsh roads, is perfectly acceptable. The car itself is an excellent choice and will hold its own in good company, as well as providing fun ragtop driving at very reasonable running costs.
Welcome to the site.
