How do I convince my landlord to allow us to have a dog?

My girlfriend really wants to get a dog but my landlord does not allow pets. Some positives we have going for us is that Ive lived in their rental for almost 15 years now. We also take care of the place and dont ask for anything extravagant, only for things that absolutely need to be replaced so we are definitely good tenants. I guess they had a problem before with a previous tenant that their animal completely ruined the carpet. I was thinking about offering an extra $1000 deposit, which would cover any kind of damage a dog could cause if any were to happen and they already have my original $800 deposit as well. Also agree to get the carpets cleaned every 6 months, which we already normally do once a year. We take exceptional care of the place, and the last couple of times theyve come to check out the place, theyve given us compliments on how nice the place is. What more can I do to convince him that we are responsible enough to have a dog and to be able to take care of the place with it?