Do you need the finish to be "flexible" or secure?
3M do some really good glues, which bond well, but still give a flexible finish. I've mainly used their foam and fabric glue (can't think of the product number right now). You can buy it in Bunnings.
The key is to spray it like a spiderweb, not too thick, and then wait until its tacky, and then stick the bits together.
But if you don't need a flexible finish, there are probably stronger glues available. Bootmakers glue was the other one we used. But again, wait until its tacky before sticking together... even use a hairdryer on it to heat it up a bit before sticking.
Pen