What tire size do you guys recommend for 18's on my lowered 2007 Mini Cooper s. It's lowered on h&r springs. Right now I'm running on 17" ssr wheels and 215/45/r17, the rear passenger tire rubs when I have passengers in the back. Will 215/40R18 work?

 

The Breyton Race GTS-R Mini wheel is 18x7" et40
tirerack suggests using 215/35-18

A good example of that would be the Continental ExtremeContact DWS
215/35-18 $149 each on special at tirerack, fits 7-8" wide wheels, 540 treadwear, 23.9" tire diameter

215/40-18 is a little taller than OEM at 24.8" and is about the same as your 215/45-17 which is rubbing. I would expect 215/40-18 to rub.

Another size that should work for you is-
205/40-18 which fits rims 7-8" wide, tire diameter 24.5" which is nearly OEM.
Michelin Pilot Super Sport Max Summer tire comes in this size for $172 each. An Excellent street tire but not for cold weather or any snow. Compared to the 215/35-18 tires the Pilot Super Sport would give a more comfortable ride.