You can install just about any modern transceiver, in just about any vehicle. If there are any qualms, it would be hybrids. The vast majority now traveling our roads, are Toyotas. Even the 2008 models just arriving are very noisy RFI wise.
The Cooper, like all BMWs, uses COP technology, so the ignition isn't too much of a problem as long as you bond things well. The body material is rather thin as most newer models are, but you can always use a trailer hitch mount for the antenna, albeit not an ideal location.