Dad? Is that you? lol.
My pops had a 1990 Camaro IROC-Z (great car, I loved it), but he hated the harsh ride and noisy tires on concrete highways in the states. He changed out the Gatorbacks for Eagle GT +4 in a 215/60 series to make the ride smoother and quieter. It did help make the car a bit more comfortable, but it completely threw performance out the window. He did something similar with the Trans Am years later, but his problem was that he always chose the cheapest tire he could get instead of choosing the right tire to solve the problem.
This question always kills me. I could respond with the usual - You should have bought a Camaro ZL-1 or Cadillac CTS-V with mag-ride, but clearly that isn't the answer that you are looking for.
So I will try my hardest to be nice, and stick to the facts of what you want, even if I strongly disagree.
As mentioned above, you can choose to go to a narrower-width tire with a taller side-profile, which will help to give you a bit softer of a ride. Any tire shop should be able to figure out the overall height of your tire, which is going to determine your speedometer accuracy. I'm not really used to going down in size, I usually go up, but when I do that I typically use the general idea of one profile size for every two width sizes. This should work in reverse as well.
I think your car should have 285/35-19 in the rear and 245/40-18 in the front? Personally, I wouldn't go lower than the 245s, and a 40 series is not too harsh of a ride. The 35's in the back are a bit hard, so you could go down in size to a 275, and up to a 40 profile. Perhaps even a 45 profile if you like, especially if you want to change to an 18" wheel out back. It might give the back end a bit more rake, but only the most scrutinous eye will be able to tell. The trouble with going narrower in the rear is that there aren't a lot of manufacturers who make tires in a 265 or 255 for sports cars. A 245 would allow you to run a 60 series tire, but it makes me want to cry to think of a wagon wheel like that on a Corvette.
So before you get too far set into changing tire sizes, understand that a big part of the ride and sound is also in the density of the compound. A hard tire that is designed to stick with heat (Goodyears are the most noticeable to me) will have a hard and noisy ride. A softer compound will stick better and at lower temperatures, be smoother and quieter, but will not last a long time (replace tires at 10-15k). Everything is a compromise. Choose your poison.
There are a lot of guys on here that have changed out their tires for various reasons, and I'm sure a few will post up their opinions, so just be patient and wait for more input. The Michelin Pilot Sport stands out in my mind as a fantastic tire with good ride while still maintaining excellent adhesion and performance. I personally run Nitto Invos and have been pretty happy with them as well. Decent price, smooth and quiet ride, and traction is decent after you warm them up. Initial traction is not great but I make well over 500hp, so traction is relative. For regular driving, I would absolutely recommend them. I've gotten more than five years out of mine, and that is very impressive.
And if you ultimately can't find anything to make your ride comfortable enough, I have a nice Cadillac that I'd be willing to trade you.
