Wheel diameter doesn't matter, it's tire size that will cause rubbing. For stock bodywork and zero offset wheels, 205/55-16 seems to be a sure thing. I run 16X7 0-offset Panasports with 225/50-16 Bridgestone RE11-A rubber but my front valence and rear fender lips are trimmed.
I ran 16X7 +6 Panasports on my previous Z with 225/50-16s with no rubbing issues, although I was running an aftermarket air dam. Also keep in mind that tire width can vary wildly between makes and models of tires, Tirerack is a good resource for more true-to-life numbers as they actually measure the tires so that you can compare apples-to-apples.
Here are some common tire sizes that match OEM diameter and should fit the wheels wells. It succinctly describes the current situation of running smaller wheels than 16". Using Tirerack to evaluate availability:
14": 195/70-14 - No performance tire options
15": 205/60-15 - One tire, Yokohama A048 (R-compound, not for cold weather or standing water)
205/50-15 - Lots of great options but a much smaller tire diameter than stock
16": 205/55-16 and 225/50-16 - TONS of great options
In short, are there tires available in the proper sizes for 14" and 15" rims? Yes.
But if you want anything else besides cheapo econo-car tires or truck rubber, you need to go to 16" or run a non-factory rolling diameter tire.