Obviously painting or power coating your original wheels would be cheapest, but it depends on your budget. One thing I would say is that the R112 (the wheels you have, as do all second gen
JCW spec cars, and newer ones with the equivalent of the old Sport Pack) are really common now, both in silver and black.
The absolute best looking MINI wheels, in my opinion, are the original
JCW alloys - see
here.
I think you can still get them from a dealer, but only in silver, and at a considerable cost. The best route would be to find a second hand set, on eBay perhaps, and in need of refurbishing (thus cheap), then get them done in black. Only seen these wheels in black once before and they look amazing! That was years ago too, when it was still a fairly "new" wheel, and before EVERYONE was doing their wheels black... the guy was seriously ballsy at the time as they were brand new out of the box and nobody was entirely sure how they'd look!
First choice from current, readily available wheels would be the R105
JCW alloy in black (like
this,
this or
this). You can see all of the OEM MINI wheels, along with common names, colour options and "R" numbers in the FAQ
here.
Another option (probably my second favourite MINI wheel ever) is the Alpina offering. I've only ever seen a handful of cars with these wheels on! If you're unfamiliar, check out the very bottom of
this page. Possibly a bit too fussy for some people, and almost definitely wouldn't work in black (in my opinion anyway).
My New JCW 
