Cats are one of the top problems for bird biodiversity in the tropics and bird populations worldwide. The most sustainable way might be to eat them, but no one in my community seems to care for that solution. Spay and neuter - ing could work, but we need to vastly increase the number of vets and the education level in the rural populations. What are some possible solutions?
Culling helps, may sound harsh but if an apex predator such as the cat begins to predominate or explode in numbers you will have reduction in populations of species that this predator preys on so reduction in the population of the apex predator will see an improvement in the species being affected.
A less unsavoury approach is to carry out non-lethal thinning of the population by trapping them and taking them to a shelter. That way if they can't find homes then the shelter will be forced to put them down.