I'd try contact cement. But there must be other kinds that will work equally well.
Before you try to repair it, I'd put some of the glue on the good side of a piece of scrap...and see how it reacts with the vinyl. You don't want a glue that's gonna eat the tile if some of it oozes onto the good surface.
Good luck.
Have a nice week...
Trent©
What do you call a smart blonde? A golden retriever.