In city varmint removal suggestions?

Need something to silently take care of rabbits & squirrels that are taking over my backyard. Any suggestions? I am thinking maybe an air rifle or pistol. Living in the city.

They do make some very good air rifles but they're pricey. Otherwise .22 CB are very quiet and snappy.
Or squirrels would be very easy in a Havahart.

Dog

I'd love a dog, but I would have to get rid of my wife.

Dogs are great, until they die. If you love your dog, that's a very tough loss to take.

I've had a few and I know the feeling.

Boxes with traps inside conibears or coil springs. I think the name is koro that makes a good squirrel trap. Just get them used to going into the box to eat and then set em up. Out of sight from prying eyes. Rabbits can be caught in wood box traps or cage traps I've used body grips on the farm years ago in trails but in town I wouldn't do that. Good luck. The wife wont let me catch anything she can see from the house. Says they are yard critters and she likes them so then I've got to be REALLY discreet. When they start to become a problem. Traps in log cubbies in the wood pile I've done cage traps in the yard waste compost pile, new bird house with an extra wide opening lots of possibilities. Have fun!

Don't have many rabbits here, but squirrels are easy to catch in cage traps.

I put a peanut in the back, a peanut near the entrance and a peanut twist-tied above the pan--Duke 5x5x16" cage traps.

I really wanted to reply, but Trapsetter said it all.

Well..... Some here might see that as an upgrade.

I would not use any form of foothold or body grip. This is where you will find potential liability. A cage trap is the way to go. Squirrels super easy. Use corn. Rabbits are tougher especially in summer when natural vegetation is green. Carrots, cabbage or brussel sprouts.

cage traps

Yes lots of cage trap options