If the CoyoteVest is slipping side-to-side on your dog it probably means that the waist band is too loose. Just like a belt used to hold up a pair of loose pants, the waist band needs to snug -- but of course not so tight that it hurts.
Nevertheless, some dogs are very round, or have very slick hair, or have an unusual gate -- for whatever reason the vest might still slip even though the waist band is snug. If you are having this problem a set of anti-slip straps can fix it.
The idea is to keep the vest centered with elastic straps that go underneath the legs on either side of the dog. The straps can go under the front legs or the rear legs -- your choice -- but the rear legs usually work better. The straps are attached to the vest with a small piece of Velcro that can grab onto the spikes or the collar stay.
To use the straps, first use a pencil or a toothpick to push one end of an elastic strap through the hole on a piece of velcro, and then tie a knot so it can't slip out. The knot should be on the fuzzy side of the velcro. Do the same thing on the other end of the elastic strap -- but don't tie a knot just yet.
Now you can attach the end with the knot to the vest (as shown above in first two pictures). Then take the other end, pass it under the leg and attach it, and pull the elastic though the hole until you get the correct amount of tension (just enough to keep the vest centered). Now hold the strap in place, remove it from the vest, and tie a single loop slipknot on the loose end of the elastic. Do the exact same thing to the other strap -- it's important that both straps end up being the same length. The slipknot makes it easy to make further adjustments if necessary.
Once you have the strap length properly adjusted you can leave them on the vest and use them whenever you put the vest on your dog. Be sure to attach the straps at the same position on either side so that the tension is balanced.