We will not  be allowing pets in this property.Any advice would be helpful

Like house rules,sub leasing,pets and so on.

I have a separate pet addendum and approval of pets. 

Carefully consider if you will allow tenants to have pets and what kinds, if any.4.

Although  my lease states no pets, they are asking if I would reconsider.  

Seems like a deceitful way to get her pet in the house.  

But to answer you question, here are some of my criteria (Note that these are neighborhood specific, so it may be different for your neighborhood):* 600 or higher credit score preferred but not required* History of stable employment preferred* No Smoking* Combined monthly gross pay must be at least 3x monthly rent* Pets may be considered with addition rent and deposit* No prior evictions or feloniesI try not to make a list too long so I end up with one tenant inquiring.

We have a clause in our lease agreements that requires tenants to obtain a renters insurance policy and also send us a copy of the declarations page every 6 months.We don't specify limits, as the amount of coverage is largely dependent on the value of their belongings.We also require a pet rider on the policy if they have a dog in the house. 

In addition, some other addenda may apply, such as: Utility Transfer Agreement-1 page; Pet Agreement-1 page; Service Animal Agreement-1 page; No Smoking Policy-1 page (This is more in depth than what is in the core agreement, used when converting a tenanted property to no smoking or when we catch someone smoking on our property.); and other addenda from time to time specific to the property or specific to the tenant.We aim to make our rental agreements easy to read, easy for the tenant to reference, easy to file, and easy for us to use in court in the event of an eviction.

I had gone against my no pet rule and allowed them to have a rabbit.