Caution with superglue! It works very well... but it can also be destructive if you are messy with it.  Make certain it doesn't seep through into the mouth.  The best way to do it is to get plastic mesh, lay it on top of the bill (small square, size of the area), then superglue that down on top of it on both sides of the break.  Eventually, it will wear off and the break may have sealed back up (no guarantees). Its effectively a cast.  Thats what you do with broken turtle shells as well, works really well.  It'll require 2 people, one to hold it in place (including the duck, so maybe 3 ppl) and the other to apply it.