When replacing tires on a Corvette you can go one of two ways, either run-flat tires or non-run-flat tires. Run-flat tires are Original Equipment and the vehicle doesn't have a spare tire, but many Corvette owners use non-run-flat tires.
Here are some popular run-flat tire choices:
Michelin Michelin Firestone
Here are some popular non-run-flat tire choices:
Hankook Continental Michelin
A ContiComfortKit will air up your tire and seal small punctures if needed. This is a nice tool if you choose non-run-flat tires.