Hi Otto to reinforce the previous post the rubber does not generally degrade and cause play at the wheel, it's more likely that the swing arm spindle is loose in the frame and the spindle nut is loose as well, and the only way to really fix that is to either renew the spindle (which is a pain as usually seizes in the blocs) or fix the frame holes, depending on which is causing the play.
Or do the swing arm spindle nut up VERY tight
In my case a groove had worn in the spindle where it passes through the frame, probably as the bike had been ridden with the spindle nut too loose for a while, and it was a real mission replacing the spindle and blocs, I posted some pics on the forum on my experince doing the job.
A quick test to see where the play is coming from would be to remove the spindle nut and yank the wheel side to side, you might see the spindle moving in the frame holes, in which case you will know the source of the problem.