Looking for quietest load and gun combo that doesn't involve a can because I refuse to pay the stamp.
Nothing .22 or .25 because they won't harm anyone.

Get your favorite single shot rifle and have it re-barreled for a cartridge called 45 Cowboy. It's the 45 Colt case shortened to 45 ACP length, used by the Cowboy Action shooters for very light loads using the 45 ACP cylinders in Ruger Single-Actions. Use a very long barrel, 28 inches or more, and it will be very quiet as the pressure will fall to very low levels by the time the bullet leaves the long barrel, yet the heavy bullet (load 255-325 grain lead bullets) still hit hard.

So 7" judge won't do the trick?

Just go with a pistol caliber carbine, like an Mp5 clone or something

20in lever action 44mag using 44spc factory or 44mag subsonic handloads.
A 357 would be quiet too, but size does matter.

This. H&K style delayed blow back
with a 16" barrel is at least as quiet
as a 10/22, if  not more so with 115 gr.

No hearing protection required at all
when shooting outside. I haven't tried
it indoors.

Very quiet.

9mm PCC with 16" barrel. Not hearing safe, but tolerable in an emergency.

Can cannon and 5.56 blanks...just don't miss since it's a muzzle loader.  I've always wanted to get one and 3D print

But in all seriousness a 45ACP or a .300blk firing subs will be about as quiet as you're gonna get.

Don't refuse to pay the stamp.  It's awesome.

smaller bores and lower pressure cartridges are going to be the most pleasant. 300 blackout handloaded with pistol powders below the speed of sound from a longer barrel would be pretty quiet and a big long bullet would do decent damage.

If wanting to stay with an AR you could have someone make you a shortened gas system to use fast burning powders and subs from a 16"

Lever guns like mentioned are also handy in such regard.

As for terminal ballistics your going to be in pistol ballistic territory so you have 2 avenues premium bonded expanded bullets or wide flat hardcast bullets to penetrate deep and crush tissue.

Some notable loads come to mind 357 mag levergun loaded with 200gr rnfp hardcast loaded to 357 mag length in 38spl cases

I once loaded a hi-point 9mm carbine with 158gr kieth swc over 3.2gr W231 and the bolt clacking was the loudest noise. velocity was around 980 I want to say and man did they hit with authority (punched perfect holes in paper too)

45 colt can be a fun too with a 255gr keith over a few gr of bullseye and remember a 255gr bullet at 900 ft/sec put alot of people 6' under

A 450 bushmaster could likely be loaded to equal hotter but again bigger bore, more powder, more pressure = more boom

Big bores are louder

Lever gun in 38spl running subsonic ammo. 158grn or heavier semi wad cutters will do the trick

ETA: beat great minds think alike

44spl out if a lever action is pretty fucking quiet.

https://imgur.com/gallery/fWzUcSf

Suppressed MP5/clone.   I’m intrigued by the new Marlin 1894 CST.

"quietest" is not the same as "quiet enough". If there was a magic load/gun combo that was quiet enough and effective enough to use indoors for hd without a silencer, people wouldn't bother spending all they money they do on silencers.

Nothing you'd want to use for hd is going to be "quiet enough" without a can. And no, I wouldn't want to use a 28" single shot cowboy rifle for hd.

If you can’t/won’t buy a stamp, consider buying a high quality set of electronic hearing protection muffs. You can then use your preferred weapon/load combination but protect your hearing. PRACTICE donning your muffs as you grab your HD weapon.

Not only will they preserve your hearing but being able to hear the police when they are screaming at you to put the gun down once they are on scene in response to “man with a gun” is probably a good thing too.

In addition, the good sets will also amplify normal conversation, so it may give you a better idea of who and where are the intruders in your house.

Not “just as good” as a suppressed weapon but better than choosing a poorer performing firearm/load.

It is critical that you practice your home defense drills to include donning and using you electronic hearing protection if you go this route.

A knife or sword is plenty quiet or buck up and pay for the stamp.

Russian silent ammo is what you want.

https://www.forgottenweapons.com/russian-silent-ammunition/

16 inch AR9 with 158 grain standard load cartridges..
And a buffer heavy enough to just cycle the action.
Add a linear compensator, to help to be quieter to the shooter.

You've already got some good suggestions. The best value to me is an 9mm AR. Not the quietest or most powerful, but still reasonably powerful, low cost, and reliable firepower. Next would be a lever action in 44 Magnum, but loaded with 44 Special. It is pretty powerful even with subsonic ammo, and with full bore 44 Mag loads, it is a viable hunting rifle. This is a great choice, but just a little bit slower than a semi-auto. With 44 Special loads it will be the quietest of these 3, to the OP's original request.

An AR in 45 Auto is a nice balance of firepower and noise. I put one together with a 16" barrel, and with basic ball ammo it remains subsonic and fairly quiet. After I adjusted the buffer weight, mine has been completely reliable. Parts to assemble it are not as widely available as for a 9mm AR, but they are out there. Once you put it together though, you are set.

I assembled a New Frontier Armory 45 glock mag lower and BCG, with a Faxon barrel, and mine has been a great shooter. But honestly, I just use the 9mm more because the ammo is cheaper. The 45 runs perfectly, and would be my preference for self defense. There is no mistaking the impact of the 45 vs. the 9mm on the steel targets at my range. The 45 hits much louder and knocks the steel around more. I just happen to use my 9mm ARs a lot more because of the ammo cost. The 45 AR has a little more recoil, but really you are just feeling the push of the heavier buffer and bolt as it cycles.

I also have a 10" 45 Auto AR pistol. It is short and handy, and with my buddies suppressor, it is ridiculously quiet with cheap 230 grain ball. (edited to clarify my post)

PCC with subsonic ammo.

9mm w/ 147s
45acp w/ 230s
357 w/38s
Etc.

E file + Form 1 X 2 =

I would think that a .45ACP pistol-caliber carbine would be much quieter than a 9mm, because they both have approximately the same powder charge,  but the .45 has 66% more bore volume.  I have not verified this scientifically.

This.  Cans are the best firearm accessory there is.  Wish I got into the game 25 years ago, but gun store BS and fearmongering kept me away for the longest time.

Yeah, don’t buy the stamp, that’ll show ‘me when you have permanent hearing loss.

Just use your Trump Change to buy a can + stamp. It’s a free gift from the government via a handout. Take it. Enjoy it. That’s the way to stick it to the man.

I know it’s now a gun but how about a crossbow or maybe big bore integrally suppressed air rifle.

You guys are lucky that you can pay the stamp and get the can. In my state (IL) there is no option to get one.

Something subsonic in pistol caliber or 300blk.

Cat sneeze loads and heavy for caliber bullets in a lever action are very interesting. Fast burning powders are used.