I should start by saying that I have no practical experience as to whether this idea will work or not for a shock dampener. I have made a hydraulic cylinder for controlling the down feed on a horizontal band saw using the same basic construction methods and it has worked well.
The appeal of this method would be that you can size it to fit your application and use commonly available materials. It assumes that you have the means to perform the simple machine work shown. If it doesn't work, you are only out a little time and a few bucks, or quid or Euros, or whatever you fellows on that side of the pond call them.
The basic idea is to transfer fluid from one side of a piston to the other by forcing it through a small orifice (or multiple) at such a rate that it tends to resist the oscillations of a spring that it is connected with. Manufactured shocks have quite a bit of technology to accomplish this, but getting down to the basics is what you were hoping to achieve. This is just an idea that originated by that stipulation.
The body of this part is made with a piece of thin wall D.O.M. or 4130 tube. The tube should have a very smooth I.D. so that no honing is necessary. The solid end is machined from bar stock and can be configured so that a mounting can be achieved at the center point of the frame. I've shown the seal end as being threaded into the tube. A little single point threading job. The seal would need to be acquired to match the diameter of the piston rod. Apiece of drill rod would have a nice ground surface for the seal to ride on. The piston is merely a piece of bar stock that is a couple of thousandths smaller than the I.D. of the tube. A hole that is one size smaller than the piston rod diameter is drilled and a groove for an O-ring is cut on the O.D. The number and size of orifice holes is where the experimentation comes into play. Start with as few as is practical and as small as possible. I would think that the fluid would need to nearly fill the cylinder as to keep the holes submerged and the fluid being moved rather than air. Mount the unit horizontally and feel how it reacts to pushing and pulling as compared to a regular automotive shock should give some indication as to whether this idea has any merit, I would think.
The drawing was sized with a 1" x .065" tube that is 5" long with a 3/8" piston rod turned down to 5/16" and threaded for a lock nut. The piston is 7/8" diameter that is turned down to .868" and is 1/2" long. The O-ring is 3/32" x 25/32". Each end piece is made from 1" cold rolled bar stock. The holes in the piston are 1/16 " at 3 places for a starting point.
I don't know if this has any value or not. It started out as just an idea and remains that way at this point. Should this seem worthwhile to pursue on your part, I would be happy to help in any way that I can.