This is some advice from experience but mostly from a podcast that I heard on BP... and a question that I don't know the answer to.
1) Can you end the tenant's M-t-M lease giving them a one-month warning? If it's a good part of town, then that is really good news, and it shouldn't be hard for you to keep it occupied. I owned a personal residence duplex and I was always able to keep it filled without missing a month and I only ever used Craigslist. I don't know where you live at all though.
2) Maybe be willing to accept the pets (in the future) but make sure that the owners give you an extra-large deposit when they move in, and then charge a little extra each month for Pet-Rent. These things should help you to financially be able to deal with the animals.
3) Make sure in the future when you're screening your own tenants that you do a better job than this guy did. haha. Get their credit scores (make them pay for this) and call their past landlords to check them out.