The HW95 or Beeman R9 (almost the same rifle) either of those would be GREAT. Enough power for squirrels, but not so much that they're hard to cock or are overly hold-sensitive.
Might be a little loud though. That's the tricky thing. Are you looking for quiet enough not to ANNOY your neighbors, (assuming cool neighbors or a rural home) or quiet enough so they won't even know you're shooting and call the cops on you? Some folks just can't get over the idea that you're shooting in your backyard, and their windows, pets or children may be in danger. Others will be like: "Oh, you can kill squirrels? Good, because I've got pesky ones too.."
If it's the first, the R9/HW95 would probably be OK. If it's the second, probably not. In that case, you may want to get a Benjamin Marauder, which is just a bit more, but has a properly quiet moderator. With that one, you pump it up to 2500 psi, (a lot of effort, that first time) after which you get 30 good shots down to 2000 psi, and re-pump it up to 2500 psi. (not bad to pump from 2000 to 2500) The Marauder (and any pre-charged pneumatic [PCP] airgun) is easier to shoot accurately than a spring piston air rifle, and it makes a lot less noise than a springer with equivalent power. Head shots on squirrels at 15 yards can be taken, even if you're standing and shooting offhand. If they're further out, the gun makes enough power (18 foot-lbs) to take body shots. (upper chest only)
One word of caution for backyard hunting: be mindful of your backstop or lack thereof. Squrrels in a tree at a low angle to you will be mostly off-limits, because if you miss, the pellet will go hundreds of yards downrange, with lethal energy. (even .177) If he's against a tree trunk or at a really high angle, you're generally OK. Some people will set up a squirrel feeding station near a good backstop, just to avoid this scenario. All you need is a pile of walnuts in front of a piece of plywood.
Here's my .177 Marauder; it will shot sub-1" groups at 50 yards all day long:
Here's a pellet I recovered from a squirrel I shot through the head yesterday. It entered his left cheek, went through the head and shoulder. It was just below his skin on the exit side when I skinned him.
