I think most of those super doublesided sticky tapes will work.
Assuming the phone case is hard plastic I'd try and find tape that has a foam sandwich to it to help with the vibrations - like the gopro sticky mounts.
Is the double sided stuff that sticky? I can't say I've used that kind of thing since the days of Blue Peter. I was thinking of a lump of araldite maybe.
I think most of those super doublesided sticky tapes will work.
Assuming the phone case is hard plastic I'd try and find tape that has a foam sandwich to it to help with the vibrations - like the gopro sticky mounts.