How do I politely deny someone's request?

I agree with the others that you handled it appropriately. I don't have a dog, so I would have said something to the effect that 'I apologize, but as stated in my profile, I don't board dogs that are not fully housebroken, and your profile says that little Fido is not housebroken.' I do the same type message when my calendar plainly shows I'm not available. That way they are gently reminded to look at my profile.

It sounds like you handled it well. I thank the person for contacting me about their pet, even if it's a pet that my profile clearly indicates I don't care for, and then let them know that I'm not the right match for ... (fill in the blank- i.e. cats, dogs of a certain age or size or that haven't been spayed/neutered/fully vaccinated, etc.) I also advise them that Rover support can help try to match them with a sitter who best fits their dog's needs, for no additional charge.

You've done the right thing. Just tell the client that their dog is not the right fit. You can suggest they use the Search filter to look for a sitter who does not have a dog and/or one who only accepts one dog at a time. Some people just don't read the profiles or are unaware of the filters for searching. You can also refer them to Rover Support as Deb suggested.

I make it very clear in my profile that I only accept dogs that are housebroken. However, many seem to think that pee pads qualify as housebroken. I have had to add that pee pads are not acceptable. I have no qualms about telling owners the reason. Just state the fact politely and assure them that they should find another sitter here on Rover that meets their needs.