The simple answer is "no," if you value the little critters that make up so much of wildlife. First, cats are not just bird killers; they are a threat to all small animals, including shrews, rodents, frogs, salamanders, lizards and snakes. Nonbirds may outnumber birds in the average cat's diet. But they still catch and kill enormous numbers of birds.
The statistics don't lie. Sixty pet kitties in Athens, Georgia, were provided with Kitty Cams that recorded everything they did for weeks at a time. The results were disturbing: cats bring back to their owners only a fraction of what they catch. Therefore, predation estimates based on observed captures were way low. Extrapolating from their predation rate and the number of cats out in nature, they probably kill at least 4 billion small animals annually in the US.
What can we do for the small native creatures that we have already put at such risk by taking away much of their natural habitat? Clearly, the best answer is to keep all pet cats inside and to have a rigorous control program for feral cats. TNR (trap, neuter, return) programs, supposedly to control cat numbers humanely, have usually led to increases in local cat populations.
Short of that, I think it is still possible to make your yard a little safer for birds in an urban setting. The most obvious way to do this would be to stop feeding them, as any congregation of birds is irresistible to feline passersby. Oh, so you don’t wish to stop feeding birds? I share that feeling, so in our yard we feed them only at certain points, usually near thickety plantings so they have some chance to escape the ever-present Sharp-shinned Hawks. The adjacent shrubbery is surrounded by chickenwire fencing at least three feet high so cats can’t hide in it and rush out on feeding birds. Even here, you have to be careful that the seeds that fall to the ground don’t fall within the fence line, attracting birds within reach of pussycat paws. Vegetation can be used to hide the fencing, so your yard doesn’t look like a prison camp.
We let our cat into the back yard on a regular basis, but only when we accompanied him. Fortunately, he had no interest in scaling the wire fence that rings the yard (perhaps getting outside was a sufficient treat in itself), and we watched him closely enough to discourage him from hanging out by the feeders. Unfortunately, of course, the perimeter fence doesn’t keep neighbor cats out of the yard. It helps if people are home enough to be vigilant catwatchers. Our solution any time we see a cat is to run from the house at it, screaming like a banshee, and subsequently all we have to do is open a window for the intruding cat to disappear like magic. We wouldn’t dream of hurting a cat, but we don’t let them know that.
What troubles me is that there are many cat lovers who are not willing to restrict their pet’s activities, and who are willing to accept whatever level of wildlife mortality that entails. Kitty is considered just one of the family, not a killing machine unleashed on the neighborhood.