I don't own a suppressor, but might for deer hunting out to about 100 yards. Effectiveness and quiet are the priorities. I don't handload anymore either, so I'd use factory loaded subsonic ammunition. Some cartridges that come to mind are the .300 Blackout, .350 Legend, .45 LC, .45-70... Are the .30's and .35's quieter than the .45's or being suppressed doesn't it matter? Lots of rifles are being threaded for suppressors today, so what would you pick for quiet deer hunting?
I've dealt with this same issue. If you handload you can make lots of stuff work, but if you're committed to not handloading anymore it's tougher. 300 BLK is the easy button: plenty of (often wimpy, though that is changing) subsonic ammo and the right twist rates for dealing with said ammo.
Of the others you mentioned, 45 colt with very heavy bullets is what I'd pick (heavy to keep the velocity down). The issue is going to be keeping things subsonic from a carbine length barrel. Even very wimpy 44 special loads tend to break the sound barrier from my 16" 1894.
If you decide to return to handloading, you can make do with just about any 300gr+ pistol bullet in 44 or 45 caliber. Started at 1050 fps at the muzzle you'll still have decent killing power out to 75 yards or so and good penetration as well. Between 75 and 100 there will be a lot of drop. Make sure your chosen platform has a fast enough twist rate to spin the heavies.