I have a 06 Cooper S Convertable and looking to change the wheels from a 205/45/17 to a 205/45/18.....is this going to be an isssue?

 

Yes, Tirerack.com shows no matches for any tire in size 205/45-18. It's too tall for the MINI even if they did make it.

If you are moving to 18x7" wheels then use 205/40-18 tires-

If you don't have to use the MINI for cold weather or snow on these tires then-
Michelin Pilot Super Sport
205/40-18 $176 each, fits rims 7-8" wide, 300 treadwear, 24.5" tire diameter is stock. You can run these even if you have a lowered suspension.

If you need a runflat in the same size-
http://www.tirerack.com/tires/tires....=yes&tab=Specs