I would never feed them to my dog. That is just training her for a taste of chicken. I won't even feed her chicken dog food.
And leaving it out for coyotes and foxes is an invitation to dinner in my hen house.
I haven't killed any of my birds yet, but when I do, I plan to use the Salatin system of composting. Coyotes, rats, and such may get some of it, but it won't be because I intended them to.