Certainly the most deadly, and the least specific method, was the use of compound 1080 and strychnine inserted into meatballs and scattered across public and private rangelands in the West and Midwest.
Another method used was poison baited explosive devices called "Coyote getters" which were supposed to be very effective.
Sheep carcasses were also injected with poison and left for scavengers. This method killed off carrion eating Coyotes while indiscriminately poisoning many other species as well.
This method is being used still:
An M-44 is a hollow, 6-inch, spring-loaded aluminum cylinder the size of a tent stake, which contains a tablet of sodium cyanide. The cylinder is topped with a cotton-tufted trigger, which is swabbed with coyote attractant.
The device is planted in the ground and dirt is packed around it. When a curious animal pulls on the trigger, sodium cyanide crystals shoot into its mouth, killing it.