67 289 engine vibration

Vibrations are sometimes hard to find, any in the drivetrain (engine, trans, driveshaft, u-joints, diff) can feel like it is coming from a different spot. So I will give you some things to check starting at the engine:

1: Check the PCV and the hose
2: If you have an autolite carb, check the power valve, you have to remove the carb, do not turn it over, remove the 4 screws on the cover on the bottom between the idle mixture screws, remove the cover, if fuel comes out the power valve is bad, you can get one at your local autoparts store.
3: Check the torque convertor nuts if you have an automatic trans, remove the inspection cover, rotate the engine with a 13/16" socket, 6" extension, and ratchet or breakover bar, until one is visible, check it and then turn the engine 1/4 turn and check the next one, until you have done all 4.
4: Check the front u-joint on the drive shaft, if there is any play in the joint it is bad, then check the rear u-joint, the same applies.
5: It doesn't hurt to check your ignition timing and vacuum advance.

Post your results. Good Luck.

If you are replacing the u-joints yourself, then you are missing something in the procedure. Here are some tips, when installing them the zerk fitting should be to the inside meaning it is closer to the driveshaft itself, after the u-joints are installed they should move freely, if they are tight you need to take a blunt chisel and a hammer and place the chisel on a V in the u-joint in the direction of the cup you want more clearance to loosen it up (i do all 4 and then check it for freeness) and tap it with the hammer with the u-joint holder resting on something solid (if it sounds confusing, maybe this helps, pressing or pounding in the cups on the u-joints makes them tight against each other, I use the blunt chisel and hammer to tap the u-joint X shape to push out each cup against its clip, so to release the tension on it. Also the u-joints need to be greased, the easiest way is to grease it before you install the driveshaft is to use a c-clamp or vise to hold the 2 cups on the rear joint that would go in the diff yoke, while you grease the rear one. The only way the diff can be eating up the u-joints is maybe if the pinion bearings are bad causing it to wobble, but I have never seen this, it is just a thought. Good Luck.