Hmm, around here, as far as I know, the coyotes and deer ignore each other. Running around in the wilds I've seen tons of sign, and deer, in areas with tons of coyotes. Killing the coyotes certainly won't magically bring more deer into the area, at least not during a single season.
Around here wolves are moving back in however, they do shift the deer populations. But not nearly as much as certain construction projects (such as quarries and human habitation). The biggest problem has been many people closing their land to hunting, creating massive safe havens where the deer just hang out.
Wish I could offer advice, but I don't have enough experience hunting. And we have a two month season...so a single day without seeing a deer is no big deal.