What transmission do you have?
Bad tire, flat spots, slipped belts will be there at all speeds. Drive slowly behind long building with windows down listen to the echo. You will hear the bad tire.
If you get vibration at single low speed spot and high speed spot its a harmonic. It is basically the Resonant frequency of the vehicle. You just have to rule out causes. Usually it's in the springs as they are unsprung weight.
Vibration under load but not in coast is typically a driveline issue. Think... "Driven Gear Train". This will be mechanical gears or clutches pushing against, rubbing against, or broken, or out of round, or broken or missing bearings, worn bushing causing excess lateral or rotational movement.
Main bearings going out you will not hear, but usually feel in the steering wheel. Rods, wrist pins, lifters you usually don't feel, you hear them. Rotational issues like, drive shaft, transmission, axle, and or wheels you feel in your back side or bottom, or as Forest Gump would say..., "buttocks".
Vibration in coast is typically driveline to include out of balance rotors, drums, wheels, spacers, driveshaft and basically anything rotating.
Engine rotation out of balance can be any thing to include harmonic balancer, flex plate or flywheel, and anything else that rotates. Old school you could remove one belt at a time, with current serpentine you can just remove it. Drive and see if vibration goes away.
Rule out engine, coast down hill and shut engine off.
Rule out transmission coast down hill with engine off in gear and then neutral or clutch disconnected.
On an automatic torque converter still turns until engine at 0 RPM, so you can listen and feel for that point. So prior to or after, is there a change. Coast in neutral, nothing is turning but the planet set and or drum/shell that is connected to the output shaft. Vibration still there or go away?
Old school when DIYing it, is to use two new worm clamps for clothes drier (4 inch ). Put on drive shaft, trial and error and definite pain in the b**t, yet you can move the worm clamps toward or away from each other until you find balance point if it's a drive shaft problem. Better yet is just remove the shaft, R@R the U-Joints and have it rebalanced as previously suggested.
Coasting down hill lightly apply brakes. Vibration reduce or go away? It's rotors or drums, or something connected to rotors or drums.
If e-brake is good, coasting down hill apply e-brake very very carefully. If vibration goes away, typically it's drums or something connected to them, or rotors if you happen to have 4 wheel disc brakes.
If your trans has removable rear housing, you can remove and change out bushing and seal. Check the yoke for excessive wear and check the output shaft while still installed for excessive play. Th200 and 2004R you can't do this, but TH 250, 350, 400, 700R4, 4L60(E) and 4L80E you can.
