The one in the picture was caught using Minnesota Trapline Products MB-550 offset cast jaw, 2-coiled trap,, I use them for fox and yotes, but also use the MB-650 which is a larger 4-coiled offset cast jaw,, If I remember the MB-550 is legal for your state, I would have to check their website for actual jaw-opening width,
If you have not trapped before, believe me , coyotes are about the hardest animal to start with, they are clever, but curious, but also very paranoid and easily spooked,
they would have to be down-right starving to step foot into a pig-style trap, and it would have to be built with heavy material, as you can see in the picture that unusually large male (49 pounds) had everything he could reach chewed down to ground level, and he had only been there a few hours !!
Its too bad you cannot use snares, as they are easiest to learn to use, and also cheaper than the traps I mentioned,
If total irradication is what your goal is, wait as late as you can legally hunt/kill them in your state, and with a little fresh rain or snowfall you may be able to track the females back to the den,and eliminate the next-generation of pups at least,
Up here we "manage" the population, often stopping trapping and hunting in some areas to leave a few for seed the next year, but then I depend on a steady flow of fur-income every fall,
Check your regs about night-hunting , as full-moon clear-sky nights with a lighted reticle can be very productive, I have a Foxpro caller and use it often, but also use a variety of CHEAP hand-calls to simulate distressed rabbits,
We often will set up on multiple sides of a valley with 2-3 shooters that have established shooting lanes,and use our cell-phones to text each other to coordinate calling techniques, it has been very effective, as what one cannot see another might,