If you want to have lots of rabbits you need to control your coyote population. If you don’t they’ll pick your rabbits clean. A coyote wants a meal 365 days of the year and venison is mighty tasty.
No, this is wrong. Rabbits have a J growth pattern. That is, they have such a high natality rate that predation will not control their population. Their population goes straight up until they significantly pass carrying capacity of their habitat, then crash. It matters not the mortality rate from predation, simply cannot keep up. This is why you'll see them in abundance and then a year later you'll swear disease got 'em all. Just wait, they'll be back.
Their population cycles like that. This is why they took over Australia once introduced there. All the dingo dogs on the continent could not control them. Another animal with such a growth pattern is the wild feral hog. And, the hog vigorously defends its young, something the rabbit does not do.
Now, if you improve your habitat for rabbits, provide them cover and food, they will have a higher carrying capacity and, thus, higher peaks on their growth curve and the lows won't be as deep. Rabbits like the same things for cover as do quail, brush within easy reach of 'em to dart to, good food plants/grasses, etc. They like trees with roots to burrow under. It's hard NOT to have good rabbit habitat, though. Heck, the flourish in the friggin' desert to the swamps!
Anyway, predation is not a factor on their ultimate growth potential. You simply cannot put enough coyotes in an area to control their growth. It will never be sigmoid.