My 68 rides like lumber wagon.
I know it's not a luxory car and a guy should expect a firm ride but after a 10 or 20 mile ride I end up coming home with a few loose teeth.
I have to do something so a good starting point is some feedback from you guys.

What's your current setup - shocks, springs, etc.?

beat me to it!

for daily driving I have the Hotchkis coils on front and Hotchkis leafs on the rear, and the soft KYB GR-2 shocks(silver color) the white KYB gas-a-just are to stiff for any modified suspensions, on track days I just add QA1 shocks for adjustablity

stock up front
single leaf in rear with ( forgive me ) air shocks to help hold it up.
I know Im gonna hear it now

So, no suspension to speak of.

What size tires, do you run stock alignment, do you often carry rear seat passengers and is a stock appearance important to you?

front 225/50/17
rear 255/50/17
the gabriels are to keep me from rubbing
I would like stock ride height it's not far from that now

I have stock factory springs that have been re temered to stock specs, stock shocks, suspension and chassis, engine mounts are all rubber.
Engine dynamically balanced.
Still cnrs like a go kart, solid tight , firm ride but smooth and free of vibration.

When other have driven my car, and have driven other camaros and similar eara muscle cars, always comment its is like no other they have driven.
im a fan of the phillospy for older street cars is restore suspension back to factory specs...taking advantage of the modern compoinds of rubber bushes etc ....but since things like moren tyre construction and compounds do need changes in alighnment specs to suit.

Your rear wheel back spacing must be wrong. You should be able to keep those tires from rubbing. Get rid of those air shocks ! You won't have a decent ride until you do.

Mine rode like a floor jack.
I recently switched from monos to 3 leafs and from KYB shocks to NAPA cheapos on the rear. The NAPA shocks give up something to the KYB's in the corners but are better for the torn up roads we have around here. That and I run my BFG's at 28 psi to let the sidewalls flex a little.

The short answer is that nothing remotely ressembling stock springs will give you that rough a ride. Look to your shocks. I'd suggest a quality shock from Koni, Bilstein or the like.

If it's still got the original springs, they are probably sagging a great deal. Be forewarned, however, if you replace them with stock parts your car will sit a lot higher than it does now.

I don't want that.
If I ditched my air shocks the rear would drop a little for sure and I would need to lower the front end to match.
What would that do to the ride ?

I'd try troubleshooting in steps - first get a good set of shocks on all four corners. Then take it out (even if it's not riding level) and see how it feels. If you feel you'd like a little more spring front or rear than you can go in that direction.

LOL, sorry, I'm not the guy to ask about ride. I'm running 650 lb./in. front springs and 225 lb./in. rear springs with an aluminum headed SBC and like the ride a lot.

No wonder it rides like crap...
in effect you have neutalised the function of the springs, and over riden the fuction of the shocks...basically you dont have a suspension at all

Get you springs reset by a good spring forger who will be able to re set for a given height, then add a good set of shocks, new rubbers etc etc.

Do it once do it right, dont mess around with patch up crap like air shocks.

Lowering the car shouldn't affect the ride.

My suggestions are:

JC Whitney 3 leaf rear springs.

New front coil springs and cut them to get your desired stance or get Hotchkis 2" lowering springs..

Monroe gas shocks... You will get all 4 for the price of 1 performance shock.

Decide what you want your final stance to be. Lowered all the way around, front raked a little, stock? Then find combos that will get you there. Some have suggested going with JCW 3-leafs. I went with them also. What a difference. Change all your shocks. Maybe go with a lowering front spring. I went with Eibach. You didn't mention whether you have changed ball joints or any other suspension pieces. How about the subframe bushings? All will effect how the car rides and handles. And all you can do yourself.