What do you mean by 'vinyl'?
Pliable Upholstery type material or unbendable tap plastic type material.
If your referring to diner booth, sit on it vinyl, then I would recommend sprayable 3m contact adhesive or brushable weldwood contact cement. Both products work great.
If you are referring to unbendable tap plastic type material i've sucessfully used titebond II wood glue. Scuff up the glueing surface, apply glue and clamp.