I once tried renting with pets, but they didn't pay their share of the rent
Yes, but they return the thanks with love and kindness. Seriously though, my wife and I have always rented with dogs. We now have three and are lucky to be in a DHA house, but in the past we have never had any issues. Probably the best thing to do is have a reference from previous REA or landlord. Failing that, offer to place a certain amount, ie $500 with bond to cover any potention damages. I have found that most people are reasonable, and if a tenant wants to be with their dogs so much, they are generally nice people.
All the best with it,
Phil.