While a .22lr will kill a coyote instantly. My opinion is that it way underpowered for coyotes. I prefer the .223 myself. By handloading I can keep the cost quite reasonable and I am able to enjoy another hobby also. If you insist on using the .22lr check out the Remington Yellowjacket(hp and Viper . I think the Viper would hold togeather the best.
These are just my opinions. Another good option is the .22 Hornet.
Whatever you choose, you owe it to the game pursued to make a clean and humane kill.