I usually repair the vinyl on my armrests. I usually use Gorilla Glue. I sprinkle a little water inbetween the vinyl, and the foam, then squeeze a 1/8 inch bead of glue in the crack. To hold them together while the glue sets, I use packing tape and bind it tightly I apply the tape from the top, around the area that is being held in place, and around the back to the top, making a loop around the entire armrest. I use as many parallel strips of tape as needed to cover the entire area that is being repaired. The next day, I take the tape off, and clean any residue with Goof Off or Goo Gone. If the glue protrudes from the repaired area, I just use a razor and cut it off. Any glue will be hidden when the armrest is reinstalled.
I have a repaired one if you are interested.