The ideal case (for me, because I want to hear what my wooden cups sound like, in other words to have the mechanical vibrations of the driver transferred to the cups) is when the driver fits snugly into the wood of the cup itself.
If I don't have that, I would try to achieve a very snug fit with different rigid tape/paper-like materials, at best a stripe of damp wood (with properly calculated length / width / thickness) wrapped, pressed and dried around the driver.
I think wood glue would be a really good candidate. It has been used musical instruments particularly cellos and Gibson guitars. Sound transfer to the tonewood really works in both cases. You don't get the same effect with bolted on components even with maximum contact between wood parts.