OK, this intrigued me because I had just picked up a Laborator 1200 and was wondering how that coupling worked, so I dug into it a little more. To get proper access to remove it, you need to remove three phillips screws from the cover over the assembly. You'll discover the whole thing is way more complicated than it first appears - lots of little shafts and u-joints and things inside! Here is the mechanism:
The coupling in question is at the bottom. Because the flex part is a brightly colored urethane, it looks like Durst spray-painted it black to keep reflections down. That can't be good for the longevity of that material! And as you can see, it eventually starts flaking off anyway.
You'll need a 1.5mm hex key (Allen wrench) to loosen the pair of right-angle-to-each-other setscrews on each hub. Sorry, a 1/16" is just a shade too big, so US folks will have to go to the hardware store and pick up a 1.5mm wrench. (I got mine for 49 cents at Ace.) The original part on mine is a Paguag series 10 "Paguflex" coupling, with 6mm holes. See info here:
http://www.wachendorff-automation.com/encoder-paguflex-coupling-type-10-pf26.html?view=print
So the part number would be PF260606 from that source.
Here in the US it's a little harder to come up with that brand, or even something with 6mm holes. McMaster-Carr has a very similar part but with 1/4" holes, which are about 1/64" too big. The setscrews should be able to take up that slack. Here is the order page:
http://www.mcmaster.com/#double-loop-couplings/=6784em
Order number is 6183K1 with 1/4" x 1/4" bores, a little over $12. I'm going to order one and see how bad that loose fit really is. I'll report back.
Duncan