A suppressor is worth looking at, and a subsonic of reasonable bore size will darn sure kill a deer at reasonable range.
A .300 Blackout through a specwar you can hear the firing pin drop and meat pop.
Depending on the bullet, somewhere around 4 grains of Blue Dot will make a .223 Rem subsonic and very quiet. I used to shoot groundhogs and coyotes out the window with one of these loads and not wake children sleeping in the next room. Not suppressed, just naturally a quiet load. The Blue Dot loads (and Titegroup loads) scale up to larger calibers, but they get louder.
With a speed limit (1080 fps or so), the way to increase energy is to increase mass. There are some .308 bullets that expand and/or tumble reliably, and at 200+ grains energy is not bad. The deer will die. BUT you need a faster twist barrel than the 1 in 10" that most 30 caliber rifles have.
The better approach to killing deer with subsonic loads is to increase caliber and bullet weight. By the time you're at 45-50 cal and 300-400 grains, you're cooking with gas. Sure, go with a centerfire if you must, but down loading a 45-50 cal muzzleloader with a conical is likely cheaper and easier since a lot of hunters already have them and they are readily available for low prices on the used market. Yes, it is hard to clean out suppressors with black powder. On the other hand, attaching a suppressor to a muzzleloader is an easier legal deal if the rifle is not classified as a modern firearm (most are not, some are).
I've got a buddy who had, he may still have, a encore frame with a 300 whisper barrel on it. Shooting through a silencerco suppressor the bullet hitting steel was MUCH louder than the actual gun itself. He shot a doe with it off his back porch as we were cooking ribs one afternoon and she was DRT.