there was a 15" tire thread just a couple of weeks ago - Porsche has some they certify as to a number of factors - big on NVH; may not be ultimate performance, but you may not want that anyway

you can also go to tirerack and see what they have in 15"

decide if you want a race tire, a near-race tire, will drive in snow or ice; will drive in rain; summer dry only and where you are on the compromise between performance & NVH

 

Only two tires available in that size on Tire Rack. One is the Pirelli P6000 and it's a Porsche spec tire.