I can't say for sure what size spare the SLK230 has, but I'm going to assume the diameter of it's tires are probably close to those of an SLK320.
The SLK320 uses a 205/55R16 in front, and a 225/50ZR in the back. The rear tire of the Mercedes must have the same diameter as the "stock" rear tire that comes on the Crossfire, because according to Motor Trend Magazines Dec. 2003 Comparison road test of the two cars, they are turning exactly the same RPM when going the same speed. (Probably because they use the same 3.27:1 differential, and transmission). Even though the spares diameter is smaller than that of the regular tires, it must not be small enough to play havoc with the cars computer.
I've been telling people to use the SLK spare ever since I've been on this forum, and I haven't heard of anybody having problems with their EMS shutting their cars down.