One of the most misunderstood things about discrimination is that even if you can legally discriminate, it is always illegal to advertise a discriminatory preference. Discriminatory advertisement is one of the most common reasons that people file a complaint.
There’s a special checkbox just for complaints about discriminatory advertising on your NY Division of Human Rights complaint form.
Most Airbnbs don’t fall under federal ADA laws (yet), but in NY State they fall under the NY State Human Rights Laws as Public Accommodations. Under those NY laws you are required to accept a Service Dog as a way to make a reasonable accommodation to provide equal access to people with disabilities.
Considering your situation, it may not be a reasonable accommodation for you but, nonetheless, you still cannot advertise it, as advertising it is its own part of the law.
What you have to do is leave the part in that is truly informational (and legal) like:
We do not allow pets on the farm. We have eight livestock guardian dogs. The LGDs’ jobs are to protect the livestock from predators. They would consider your pet a predator and therefore your pet is not safe on the farm.
And then if someone contacts you about bringing a service dog, or even if they just show up with a service dog, then you will have to tell them that you feel that it is not a reasonable accommodation for your business and so you will not allow their Service Dog on the farm.
That does not guarantee that someone won’t file a complaint but if they do, you’ll be in a much better position to defend it if you haven’t also been illegally advertising that you don’t accept Service Dogs.