RE: coyotes killing deer
Not so sure if the sponge deal really works from a biological perspective. The yote would instinctively chew the sponge into somewhat smaller pieces. Cellulose (the material most sponges are made of) will be partially digested, but the rest would probably pass through.
Maybe putting a sponge soaked in deer blood with some razor blades in it would work if you could get the yote to swallow the blades as well and induce some Gastrointestinal bleeding!
Personally, I'd rather shoot 'em that way I know they're down.