Blow guns and sling shots and atlatls and "everything else' is of course an option but the main issue with suggesting these things is that they require specific skills/training to develop.
Yes, a firearm is something you have to develop as well however I bet that all of us here have plenty of firearms training so moving to an Air Rifle is 100% natural.
For the OP, if you want to go completely silent then get a pneumatic/pump and then work out a shroud for it. The only issue with springers and piston air rifles is that you won't be able to take the sound down enough due to the mechanics themselves making the majority of the noise. A pneumatic only makes very little noise and the only thing you are dealing with is the air volume.
And to clarify the velocity statements, you do not want your pellet to break the sound barrier. It makes unwanted noise, pellets do not stay supersonic for long and as it goes through the sound barrier and back down there is a destabilization of the pellet.
It will be hard to keep a PCP fed in a SHTF style situation but a standard pump rifle can go on forever if you get parts kits for them.
This thread is a little old, but I feel the need to chime in here.
@Jida - The PCP will be EASILY fed in any situation. dos too the PCP people have adapters for EVERYTHING! SCBA tanks, SCUBA tanks, Paintball tanks, 5500psi, 4500psi, 3000psi and other gasses adapters are inexpensive. Plus, most of the PCP people have the HP hand pump- looks like a bicycle pump.
As for actually FEEDING the air to the PCP. Most of them, depending on caliber, get 50-100 shots per filling before the shots start falling off due to regulators.
As for spare parts - thats easy. Most of the consumables in a PCP are the O-Rings. Most of them come with extras and the 'repair'/'service' kits are very inexpensive. - Anyone involved in a specific item should research the pros and cons anyways. If there is a specific reliability issue with a specific part, grab an extra one or two. - Law of rerundancy
Suppression issue. - NOT AN ISSUE!!!! Was federally ruled on many years back that since there is no EXPLOSION happening, it is NOT A GUN. So you can legally and most people do, suppress the air rifle to lower your audible signature even more.
I have taken game of all sizes in my travels with air rifles. in some instances, I have got a shot off, not spooked the animal if it was a miss and got follow up shots. If it was a HIT, and there were other animals around, I was able to get a second or third animal down to harvest all in the same spot.
TRAVELING> Tis is the biggest plus for me. I travel internationally. Border crossings and states etc. Most countries and states have no issues with them and there is NO PAPERWORK involved. Most that has happened to me was the USA border back into the states saying, "Hey, it has a scope on it"
Where i have had an issue and had a lesser value one confiscated was in NOVA. $500 fine and a $300 rifle confiscated. Some little kids were playing outside when I was walking back to a place I was staying temporarily. The kids saw me and ran up to me yelling they wanted to shoot the gun. they then said shoot me. I smiled and said "No, guns are not toys, especially AIR GUNS, You haven't seen the Christmas Story Kids?" One ran away and told his mom some nonsense and 4 min later as I am reaching the front door, I was approached and told the Lie the kids said to his mother who said I threatened their kids and told them I was going to shoot them all. - - They were all little Spanish kids in a Section 8 housing area. I hadn't even shot that day. I walked the air rifle over to a store to get the proper o-rings and have it checked out due to the little bit of spot rust I was seeing. Never had that issue in the past but it was an expensive lesson.
Check out
http://www.airgunsofarizona.com/main.html
FX has some multi caliber high end air rifles. My personal preference is the .25 or the .30 right now. The other calibers are great and you CAN hunt larger game with most of the new PCP Guns out there LEGALLY. Lots of states are adding Air Guns to the DNR regulations.
Another great forum to do some reading is
http://www.airgunnation.com
INVEST in a gun that will last you. Something you can learn how to master and not want to get rid of fast. Save your money and set it towards a nice gun. AOA will do a Layaway for you if you want. The Daystate Wolverine is an exceptional piece, heirloom quality even.
Remember, in some countries, like England, Firearms are so hard to get legally the effort is not worth it. Airguns on the other hand, are not, and they want them all suppressed there. Plus it is legal. Cans over there are very inexpensive. $20 i paid for one.