Any tire shop will gladly oblige you if you ask them for a take off, bald tire. They toss them out or have recyclers come gather them all up. Clem Tire in Madison gave me 2 bald compact car tires. Any size will do, I believe a 14" may give the coyote less area to avoid the trap pan. Any size between 14" and 18" rimmed tires should work well.
I like the tire set. It's junky looking, so I don't use it much as the property I trap is along a main road. Once a heavy rain soaks the inside of the tire, it stinks something awful. Disposing of the tire can be a pain after the inside of it has been growing algae and had coyote bait in it. But tire sets are somewhat rain proof, unless it rains sideways. The bait is protected in the tire and can last a long time.
There's no need to nail the tire down. The coyote won't move the tire until it tries getting out of the trap. Even then, the tire is too cumbersome for the coyote to do much with it.
A few good buddies have asked me for advice, so I've tried writing up some help for them. The pages of trapping magazines have better advice, but to get started the basics never really change. You learn volumes by making mistakes, like letting dirt get under your pan or forgetting to crank down on a quicklink and losing a trap. The harder lessons stick out more in your mind on the next go 'round. Tight chains!
Gun Owners of America - GunOwners.org National Trappers Association - NationalTrappers.com Alabama Trappers and Predator Control Association - ATPCA.org
Fight and stand together or lose the God-given right to hunt, trap, and shoot