Many trappers would tell you it is not a sport, but a commercial venture. Some states consider trapping commercial also, so equating it with beagles chasing pheasants may not be accepted.
Coyotes don't stay on one property only they travel through the crappy no cover spots to get to the other cover spots...so intercept them on the no cover spots and trap those instead. .. Jim
This may be the post of the year. It is a recurring theme of "how can I catch a ___ in this circumstance?" when truth is you get them on the way to the problem area. Coyotes don't fly, they have to cross some trappable location to get anyplace else they might ever be.
As to trap used, offset does nothing but let the levers get higher on the jaws, laminations do spread the pain over a wider area and thus may reduce bruising but are often coupled with increased power through four coiling, so just get a larger bruise. idk rubber but they look like regular jaws to me.
I used regular jawed two coiled traps that have the sharp rounded off the jaws and check often, one trick I have used is to set just before dusk and spring or remove the traps in early morning. More time invested but pets rarely leave home in the dark. I have also released my own and the neighbors dog unharmed, returning a pet and telling how you caught it far from home usually stops that pet roaming.