Polyurethane glues- Excel or Gorilla are great in damp conditions-
however they do foam ie expand so would suggest you use less than you think you'll need, also it is a bear to clean off of your hands, however have foud this to be very effective adhesive in situations where there is contamination from prior glues- ie @ frame and panel doors and on mortise and tenon chair joints....
Titebond II is fairly weather proof and more foregiving than the above... could apply it with a glue syringe.

More and more I'm using "Hot Shot" glues- basically crazy glue w/ shoulders, not the strongest but definitely the fastest.
hold the pieces together and hit it w/ the accelerant- it's done.

Met History wrote:

The walls in my bathroom were painted by our "expensive" painter five years ago.  The overall paint job is still good, but the boundary between the tile and the wall has failed.  In prepping this area for touchups, our "cheap" painter [that's me] noticed that the wall had been canvassed.  The bottom edge of the canvas - where it almost meets the tile - is still pretty solid, but it has curled up, away from the wall.

I am really too cheap a painter to reglue all 10 feet x 1/4 inch of this damn canvas edging, especially high up where I might fall and cause injury to my precious body.

Any ideas?

Sign me,  Please Don't Tell Me to Spray a Waxy Substance On It