Does anyone charge monthly or annually for pets?

The tenant is asking to alter the lease to decrease pet rent for just 1 pet.

People like the idea of grilling out, bringing their pets and if you get lucky, having a private pool to use.   

The costs have to reasonable/legit, but they are not capped by the security deposit in any way.As to the OPs question, I believe everywhere in San Diego county, the traditional security deposit without any special circumstances (pets, water beds, etc.) is for the security deposit to be one month's rent. 

I am rehabbing a house with pet urine stains throughout the upstairs subfloor.

I had to allow a 15lb dog in the property though but I took a nice pet fee and made strict rules (new carpet).

Potential tenants don't even get to see the place or receive an application if they don't pass our pre-screening conversations (where we talk about income, reasons for moving, job history, credit and criminal history, pets, etc.).The first person who passes the screening call, sees the place, and hands us the filled out application with the $25 gets the background check.

Additionally, extending a lease can be accomplished when allowing a tenant request, like a small pet or additional roomate, etc.

As far as the dog, again, for a healthy non-refundable pet deposit and increase in monthly rent, you'll consider letting them stay.

Your only calculations you need to be concerned with is basically your ROI for that investment.Now you can debate leveraged or not but it is a bit of a pet peeve of mine for people to think that the way to measure any investment is how long until you get your money back.