Yes, you can compost livestock, but that doesn't mean just throwing them on the manure pile. There are specifications on how it is to be done.As a funny quirk in Ontario’s manure management plans regulations, chickens can legitimately be thrown into manure piles as a matter of disposal, they’re classified as compostable....
Here's how poultry in particular are to be composted if not using a bin.
This factsheet describes the use of windrow composting as a deadstock management option available to poultry farmers. It provides specific information on substrate materials, siting requirements and compost pile management.
Note that there is specific mention of doing it properly to avoid attracting scavengers, with coyotes being mentioned by name. It also says that "any scavenging from the windrows is unacceptable" as it will compromise biosecurity.
The Compost Pile
The final pile is cone shaped, 2.4–3.6 m (8–12 ft) wide at the base and 1.2–1.8 m (4–6 ft) tall at the highest point (Figure 2). No poultry carcasses should be visible in the finished windrow; during the creation of the pile, carcasses are placed at least 15 cm (6 in.) from the edges of the pile. The cap is extremely important as it serves as a biofilter to reduce or contain odours within the windrow during carcass breakdown.
Release of odours is not only offensive to neighbours, it can attract scavengers, such as skunks, raccoons, rats and coyotes, to the compost windrow. Due to the prolonged heating of the material, proper composting will destroy most, if not all, of the pathogenic organisms contained in the carcasses. If a scavenger were to remove a partially composted carcass from the windrow pile before the process has been completed, still-active pathogenic organisms could be spread to the surrounding environment – other barns, farms, etc. To maintain biosecurity, any scavenging from the windrows is unacceptable.