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It depends on how many coyotes you hunt relative to the population of coyotes and relative to the population cycles of leporids (rabbits and hares). Both cottontail rabbits and jackrabbits (hairs) can have population explosions and population crashes that come with the availability of resources and predation. If you remove the coyote predation and if there are not other sufficient predators in the area to take up the slap, the leporid population will grow to the limits of the food resources available, over eat the resources, and subsequently crash.
If you slaughter coyotes, the population increase in leporids can take months as gestation runs about 6 weeks for leporids and litters are 1-6, usually 3-4, and can reproduce themselves at 3-4 months (as I recall).
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