a lot of times when a customer mentions a vibration issue, they automatically assume the vibration is in the engine. like anything else, you want to isolate and identify the actual problem, rather take shots in the dark and randomly replace parts based on guesses, whenever possible.
first isolate whether the vibration only happens when going down the road. if theres no vibration when reved up in park or neutral, but there is in drive, going down the road, isolate whether is only happens when brakes are applied, indicating a possible warped drum. if you jack up the car and put it in drive and the vibration goes away, look for a bent rim or bad tire. bent rims are really common on old cars, from age.... and even more common if you had custom rims made and welded together (crooked). out of balance tires are also common. weights can fly off... and just because you had the tires balanced, doesnt mean they did a good job. rotating the tires, front to back, can be a good way to isolate that. i've even seen brake drums out of balance and the weights have fallen off or they weren't balanced from the factory as a defect. if the vibration doesn't go away, check out your drive shaft U-joints, (possible drive shaft imbalance or bent?) or support bearing in two piece drive shaft applications may be wiped out. perhaps you did an engine swap and the engine/trans combo isn't mounted straight in the car? you can offset the engine, no problem if necessary, but trans needs to be moved over the same amount. radical/incorrect pinion angles can also encourage vibration and drastically shorten the lifespan of the U joint. drive shaft U joint yokes should be phases properly. engine and trans should be on the same parallel plane, BUT NOT lined up in a straight line. if so, the needle bearings won't rotate and cause premature wear. i remember my old 47, i had to change the rear U joint on every single summer because the pinion was lined up straight with the engine and trans.
if it does it in park and neutral, you can rule out the driveline as being the issue. obviously look into engine and trans mounts, and make sure the exhaust and or floor tunnel isn't hitting anything. i see people hard mount the engine in hot rods from time to time. don't do that. the block isn't designed to be a crossmember for your frame, making it a good way to crack your block. frames flex a lot, even beefed up from stock, outside of the obvious transmitted vibration without any insolation from rubber.
the two most common reasons i see when people bring their cars to me with verified engine vibration is the balancer bolt was left loose on 57 to 66 engines and the balancer has walked and shakes. under rare instances, the rubber between the two balancer pieces can fall out completely and cause a vibration. depending how the engine was rebalanced, if the balancer has spun, it can also cause vibration. even more commonly, the flex plate was bolted on wrong. these engines are externally balanced. it may not look like it, but all the stock flexplates have a counter balance. the flexplate will bolt on 6 different ways. 264/322 has a guide pin on crank so it won't go on wrong. the 57 and later does not, so you have to pay attention to the index hole dimple. you can check to see if its on right, if the counter weighted section lines up with the lopsided bulge in the rear of the flexplate mounting flange on back of crank. you can do so with a flashlight with flexplate cover removed.. also take note that the early 401 triangular flexplate is NOT interchangable with the 364 ones without rebalancing. otherwise they look very similar. 364 balancers are also not interchangable with 401s. if you flip the balancer over, the 364 has half the counterweight as the 401/425. from the factory, the 401 had a different counterbalance on flexplate and balancer. same stamping and casting, but more weight reduced via drilling. the counterbalance is so similar between those engines (401/425) that its very unlikely swapping balancers or flexplates between stock engines would cause a vibration. later on, the factory released the same replacement balancer and flexplate for both engines with the same part number. if you had your engine rebalanced with a stick flywheel or flexplate and now you want to run the other, if a project changes directions... thats no problem. just take the old flexplate or flywheel with the new one down to the machine shop and get the counter balance matched. also be aware that even if your engine has never been rebuilt and is stock... doesn't mean that the used flywheel you want to put on hasn't been rebalanced for another engine.
the same story with the 264 and 322. all 264 had a cast iron crank pulley (not to be confused with early 53 engines.) you can rebalance a 264 flexplate to work on a 322 and visa versa, but shouldn't just swap them otherwise. due to the scarcity of locating 2 groove 264 crank pulleys, we rebalance the 322 balancers to 264 specs to run 2 groove pulleys. (thats a service we provide.)
otherwise, we recommend rebalancing during engine rebuilding, even if just only pistons were replaced. never only replace 1 or 2 pistons with different stock ones with different compression ratio/casting number, always replace them as a set. be sure the flexplate/flywheel and balancer are both supplied to the machine shop to do so. its just not worth the risk, otherwise, to cut that corner. bottom end rotating assy balancing is couch change in the grand scheme of the amount of money it costs to rebuild one of these engines. transmission adaptors such as the 700 adaptor design, requires a dial indecator to be used to check spacer run out. we've even seen trans converters out of balance.
if running a manual trans, too stiff a disk can cause chattering and vibration as well, when shifting. also take note that automatics are far more forgiving of bellhousing misalignment than the input shaft on your manual bellhousing.. or maybe your manual bellhousing's hole is offset as a defect? . ive ran into the issue a handful of times, where the bellhousing required offset guide pins to center the transmission. the allowed tollerances are contingent upon the length of the input shaft. other symptoms of that include constantly wiping out pilot bushings.
chasing down vibrations is as annoying as chasing down and isolating oil leaks. its in your best interest to pay attention to all that, to cut down on problems so you won't have to do the job twice.