There are a couple solutions to your problem:
- If a chicken dies, hang it from a hot wire (enough to give you a shock when you touch the chicken) at about the height of a coyote's nose, when he's just trotting around. This will sort of train them to not want to touch a chicken.
- Get a few guineas. They will squawk very loudly when something out of the ordinary even thinks about coming near them.
- The way I like to deal with coyotes is just to shoot them whenever I can see them. You can also sell their hides for maybe around $60 where I live.
- Use heavy-duty welded wire fencing (most commonly used for sheep) on the outside and a chicken wire fence on the inside.
- 5-6 ft. high chain-link fencing works very well, but is pretty expensive for a new one.
- Trapping coyotes is also a good technique if you have the time to check the traps frequently.