Do the tenants own pets?

In the future you need to stick to your guns and not allow pets. 

Does anyone have a template for a damage rider for pets?

Some ways a tenant will search is by specific property location, rental term (nightly, weekly, monthly), a specific mile radius from a desired location like an office, rental rate, bedroom count, furnished or unfurnished, vacation rental, corporate housing, CHBO Complete™, keywords, pet friendly (or not), move-in now, map view or property type (apartment, house, etc.).Marketing IdeasPulling out all the stops to ensure your property earns high annual occupancy levels takes some time and commitment, but is typically well worth the effort.

I am also considering either lowering the rental price (below market), offering incentive (pay for some of move), and/or considering allowing pets. 

My tenant is requesting to add her boyfriend and a pet to an existing lease that I inherited.

but no, everyone wants a pet as they are isolating at home. 

Initially I was going to accept no pets on my property.

She's even pet her while visiting the house.

I suggest having the tenant select the pest control service in case he/she later claims the power spray makes the pets sick.