Well, it's not a surf board, it's a body board but who's counting?

I was given it by my cousin and it's a good board but the outer layer
(polythene?) has begun delaminating from the body (polystyrene). It's
been bodged with gaffer tape and that is doing an OK job, but I'd like
to glue it. Obviously it was originally glued with something that a)
will withstand seawater and b) is compatible with the two materials.
Can anyone suggest an adhesive that might do the trick?

Thanks

Edward