Where is the play shock or relay arm ?
If it is shock mounting bush it is only one at the top . but do not think it will be that.
If the movement is in the relay arm - Replace bushes bearings and seal/dust seal should sort it out.
Think you can get non BMW parts , see a kit somewhere.
One on eblag
Does not come with bushings for inside needle rollers. ( comes with swingarm bearings as well , price does not seem to bad for what you get he appears to have sold a few.)
If your bushings are reusable that would be nice but you will probably find they my have some wear .
You need to take the relay arm of and have a look , standard seals are pretty poor , and lack of grease cause issues.
Look at the sections
Deflection parts f rear wheel suspension
Tension struts with mounting
But remember it is an advise so would not think urgent , would strip and inspect possibly when you have time.