What Could Be Causing The Suspension Shake In My 1991 Honda Civic?

I need to assume that the car was shaking when you bought it. If it started shaking after you had work done to it, then obviously someone has done you a disservice.
If you’ve had an alignment, then I have to assume that all of the steering and suspension parts were examined properly just prior as a car can’t be aligned wit bad or worn parts. Looking at your list of maintenance, I have to say that you have NOT ruled out your tires. There are two thing tire situations that I can think of. 1) You have directional tires and someone rotated them incorrectly. 2) More probably, and very difficult do discern is the belts may have slipped or torn inside one of the tires. Sometimes it’s a situation you can actually see; sometimes not. you seem to have ruled out everything else, again, assuming someone checked the suspension before aligning it.