We have rabbits and we don't see all that much sign of coyotes. I think the lack of pheasants is due more to loss of habitat than predation by coyotes.

Pheasants are an introduced species, but rabbits and coyotes have been around together for a long time.

Look around you at all the land that used to be farms and fields that are now shopping malls and subdivisions.

There are some rabbits living in the shrubs around our house and we live in the city. But we don't keep a carefully manicured yard like some people do.