I live in the Michigan Shotgun Zone. I think someone already mentioned it, but, you can now hunt in the shotgun zone with a centerfire rifle so long as the round is .35 or larger, case length between 1.2 and 1.8", and straight walled. A .44 lever gun will do the job and do it well, but think bigger and get a .450 Bushmaster or a .50 Beowulf. I just finished a .50 Beowulf that will replace my slug gun next year, possibly retire it. This should be the perfect deer gun inside of 150 yards. It will also wreak havoc on hogs should you get to go on that trip.
If you already live in the Rifle Zone, check out the .458 socom too, especially if you plan to roll your own ammo. Bullet selection is supposed to be outstanding. Many say it is the superior big bore, but it wouldn't have served my purpose. I can't use necked down cartridges where I'm at and I don't reload.