What to do/where to take troublesome stray cats?

My grandmother has some cats living by her house that aren't spayed or neutered, so they just keep having kittens and then abandoning some of them in other peoples' yards so there are dead kittens just. Around. When she called animal control(?) she was told they only take dogs, not cats, and I've seen threads here that the shelters are at their limits.

The cats have been there for years so they're obviously feral but feral cats can usually go into a barn cat program afaik. Even if they could just be spayed/neutered and released that would be an improvement.