Have successfully hunted Coyotes with my AR15A2, Ruger Mini-14, and a single-shot H&R Heavy Barrel Handi-Rifle. Coyotes will sometimes be around in packs or groups. The more Ammunition available, the better! The Single Shot Handi-Rifle proved to be a handi-cap (pun intended), although very very accurate, and I did kill one with it, and only one, out of three available.
Coyotes up here, are very routinely hunted with AR15's in their various configurations, and a Vz58 or AK47 would not be considered unusual. I've even seen M1 Garands and M1A's used on them. Currently, I favor my accurized Ruger Mini-14, using a CCI Speer 52 grain FB-JHP or BT-JHP on top of H335 or W748. We have no Magazine Capacity Restrictions for Coyotes and other Varmints.
As for Bunny Busting, I've no experience with your Arizona Jack-Rabbits, which are a heartier breed than our local Mid-West Cotton-Tails, where a .22LR or .22 Magnum will usually suffice, and distances are usually only a paltry 50 yards, on average. However, I expect your 5.56mm Vz58 will do the job very nicely, but I would recommend some optics.
