Congratulations on the Coote! I love mine!
Couple of questions.
Where is the wobble at? Does the machine move side to side, or is the belt wobbling?
If the whole machine seems to sway, then how is it mounted to the bench/how heavy is the bench?
The base on the coote aint real big or wide. You need something pretty substantial and rigid to bolt it to. If the bench itself is flimsy the whole machine can vibrate, which is going to show up most at the top.
I've got mine bolted to a white oak 1X4 (full 1" thick, not planed) thats laminated with another oak 1X4 (glue and screws). That runs front to back on the bench and is bolted onto 2X4's that are bolted across the front and back edges of the workbench. The whole thing is really rigid and spreads the load over a wide area.
If the wobble is in the belt. Then I'd look over the tracking pulley a little bit. Maybe its not set quite right, adjusting the tracking also affects the tension a little bit. You also might try a different belt and see if you still have the same problem.
I'm really happy with my coote. I have to adjust the tracking a little bit to switch from the contact wheel to the platen, but that doens't really matter, and it does run nice and true.