What you are probably experiencing is horrendously bad unsprung weight ratio.
This is a common situation with heavy duty vehicles designed to take a load, when unloaded. It is due to the relatively heavy wheels and (usually solid) axles ("unsprung") versus the light weight of the vehicle being supported, especially when unladen.
One solution is light springs and air adjustable "overload" shocks. You used to be able to buy them at Sears - don't know where you can get them now. They had a dash mounted adjustment.
Another possible aid might be shocks that have much greater rebound than compression damping.
Yet another would be to choose the lightest tires that will do the job for you. Some "mag" wheels are much heavier than stock pressed steel wheels.
The best riding cars have very light unsprung parts, which usually includes independent suspension, since differentials are so heavy. The unsprung part of the vehicle's weight includes the tires, wheels, brakes, half the suspension parts holding the wheel, half the shocks, half the spring.
I used to own a Rover 2000TC which was optimized for unsprung weight ratio so extremely (for a street car) that the rear disc brakes were mounted just outboard the differential so that they weren't part of the unsprung weight. It took unbelievably bad roads in comfort.
