How do I glue corain to overflow hose?

Look at the "similar questions" under your post. Lots of answers.

Call any Corian manufacturer or local installer. They will tell you exactly what to use. Also, you may try silicone. If you use silicone, both surfaces must be (must be) clean. Use denatured alcohol for cleaning purposes. Pour it in spray bottle and spray both surfaces several times before you apply silicone. Gently wipe it off and let it evaporate. Then, apply silicone to both sink and overflow. Be generous in application, but not over apply. Press overflow against the sink and hold for few minutes, then allow to dry as per instructions. Use the "ultra" silicone that dries in 30 minutes ( Home Depot / about $8.00 a tube ).

Hope that helps

Milo