I admire your determination and craftiness.
I'd for sure study another bird you have's mouth for proper design.
I'd make several beaks because you'll be ready when the 1st one falls off and won't be caught empty handed.
Don't expect your 1st try to be "It". It will probably take several tries until you find the best glue, method and design.
My only concern is that the wound where the beak broke off may need more time to heal.
I'm sure your anxious to get a beak on there but I'd for sure want that all healed up before attaching anything to it.
It also may grow a bit back, changing your design later on....I hope that happens, but only time will tell.
I like what Ten Chicks said, adding a type of mesh to hold it would be a great idea. I think they do this with fixing broken fingernails. Maybe the store has some repair kits with such a mesh. I've never had my fingernails done so I am clueless to the details on this.
I did some research on glues and because you need a non-clamp type glue and one that sets quickly probably your best bet is super glue.
The only draw back is super glue is not good for filling cracks or gaps, so possibly you may need two types of glues.
One for the actual part that touches together with good filling so food/water does not get lodged and also to sturdy the base. I'd go for the epoxy(24hr drying time), then for the holding power and quick drying aspect quickly brush on a thin layer of super glue with a fingernail polish brush on a portion of the real beak and new beak, then gently press your mesh into that then finish out with another layer(s) of super glue.
Getting the chicken to stay steady will be a challenge. I know when things are dark is when they are less apt to squirm, but you need light to work on your chick.
Perhaps a cover or black sock with a hole cut in it, to where the beak only is sticking out but eyes covered???
Here are some glue rating sites I found:
http://www.diylife.com/2011/03/31/best-glue/
http://donsnotes.com/home_garden/glue.html
Good luck and keep us posted.
