[Flathead Fever]

Bias ply tires with flatspots from sitting?

Spin the tires while watching them and make sure they are not starting to separate?

Tire balance?

You can try rotating the tires.

U-joints, like everybody said?

When you replace u-joints its a good practice to keep the front slip yoke, driveshaft and even the pinion yoke in their original positions

Later year vehicles with two-piece driveshafts need to have their u-joints all lined up (in phase)

Center support bearings on two-piece driveshafts.

Bent driveshaft?

Transmission tailshaft bushing alowing the driveshaft yoke to move excessively?

Axle bearings pitted?

Engine or trans mounts making metal to metal contact? It just takes one little spot to not be insulated by the rubber mounts

See if the vibration is there while on the gas, coasting in gear, coasting in neutral?

Do you feel the vibration in the seat of your pants or in the steering wheel?

Do you feel the vibration parked, while revving the engine in neutral. Maybe something is out of balance like a clutch?

At work we would put the vehicle up in the air on the hoist and have someone drive it at 50 mph. While you stand under there next to the whirling driveshaft, wearing a stethoscope and listening to the pinion bearings, axle bearings..... I've even stuck another mechanic in the trunk to listen and feel for a vibration and gone for a ride. We would also stick the vehicle on the smog machine's dyno so there was a load on the drivetrain to try and simulate a vibration.