I need to replace 2 of the stock 195/50/16. I could get some slightly used 195/55/16 really cheap.

Any problems using this size??

 

Three problems:
1. It will affect the accuracy of your speedometer reading. Check out: www.miata.net/garage/tirecalc.html

2. The increased aspect ratio (from 50 to 55) will result in a more flexible sidewall which will have a negative effect on handling.

3. The overall increase in tire diameter and weight will result in a slight reduction in acceleration.

For best performance, replace your tires with one's of the same size unless you are also changing the wheel diameter.

Welcome to the Forum.

 

There's no problem replacing with that size ONLY IF you replace all four tires. You cannot have 2 tires of OEM size and the other 2 of different size. So if you can get another pair of 195/55R16 cheap, then go for it.