Recent property manager encouraged me to have pets and they rented to someone with a dog and cat and when I asked for pet rent they told me they keep it.

From a liability standpoint, it's a good idea, but I think it can also help increase rental demand for tenants that may have pets, small children, etc.

Pet your dog or cat.

I also send them a monthly "Friendly Rent Reminder" by email with lots of really neat pictures of dogs, cats, special notices, etc. 

They can bring all their pets and make it feel like their home.

Shortly followed by "you are discriminating against me because of the dogs". 

Pros - you got a discount of $500 off your $2000 rent and you can make your house/unit however you like, you can have whatever pets you want, and you can get capital gains free appreciation if you increase the value of the property through renovations or the market just gets better.

There is a particular demand for short term rentals that will accept dogs as many families have pets but not many rentals are willing to accept them.

I wonder how a room rental tenant with a service dog/emotional support animal would be handled?

Here is a list of documents I tend to ask for:Completed ApplicationPhoto ID (Passport or Driver's License or State ID)Most Recent Tax ReturnMost Recent W-2/1099 (If Independent Contractor)3 Most Recent Bank Statement (Showing Maximum Liquid Assets)3 Most Recent Paystubs-Student School Schedule and ID (if applicable)Pet License (if applicable)Pet Vaccinations Records (if applicable)Landlord Reference Letter (if applicable)Proof of Rent Payments (if applicable)CPA Letter (if applicable)If they can't provide sufficient documentation for you to approve them as tenants, then it would be better for you to move on to the next applicant.