An invasive species by definition is one not native to a geographical range, and that has been introduced by humans, either deliberately (as in the case of rabbits in Australia) or by accident, such as zebra mussels in US waters. Coyotes, on the other hand, are a species native to North America, and an integral part of its ecosystem. Like other canids, they are pack animals with complex social structures. They are known in Native American legend for the cleverness, and are indeed highly adaptable, flourishing in a wide range of environments. Far from being a pest, coyotes prevent overgrazing by being natural predators of deer.
In fact, the true invasive species are the herds of cattle and sheep overgrazing public lands, and subsidized by taxpayers (ranchers are grossly undercharged for grazing permits and taxpayers make up the difference).