There's this kind of part which you can get:
It's (sometimes) called a "U clamp". And there's another interesting invention called a "sleeve nut" or "sex-bolt":
So, if you:
Get a U clamp with the diameter of the larger cylinder
Get a U clamp with the diameter of the smaller cylinder
Get a sleeve-nut which matches the ...
As a hack for gaming devices such as yours, create a high-performance non-slip 'gaming' mat which sits on the surface of your desk.
The problem with small rubber feet and anti-slip materials is that dust, dirt, crumbs, body oils, etc. soon make both surfaces slippery again. They're not easy to maintain. As you've also discovered, there isn't much surface ...