[alt text: a two panel comic. In the first panel, a doctor is talking to a patient, and the patient is holding her head. The doctor is saying, "Does it hurt?", and the woman is replying, "Yes...". In the second panel, the doctor is replying, "Keep your cat inside or I'll punch you again". ]
Coyotes are the least of the concerns. Here is the real problem.
https://www.smithsonianmag.com/science-nature/australias-cats-kill-two-billion-animals-annually-180977235/