We have had a tenant that has been living in our duplex for about 2 years.  After year one  the contract goes month to month.  We no longer want them to live there.  We found out today they have a dog (we have a strict no pet policy- and when they asked 6 months ago we said absolutely not).  We are worried that they will damage the apartment (the husband has had a restraining order in the past from the wife, but moved back in without us knowing as well).  Yeah, we picked a winner (we actually thought they were great at first, with no criminal records, and fit our strict criteria).  Anyway, what is the best way to get rid of them nicely, but firmly?  She also claimed to the neighbor that the dog is an "emotional support animal".  I don't want to get into any legal problems. Help!

You just need to give 30 days notice that you will be ending the month to month tenancy.  Send it out before the end of the month letting them know they need to be out by the end of October. There is no need to mention the dog or give any reason. 

I feel you pain, I'm going through A similar situation minus the dog but adding the no paying rent issue. I served my tenant with a notice to quit, due to nonpayment. Gave her 14 days that was at the beginning of the month, she still there. Im trying to avoid going to court as my state is a tenant friendly state. Something I've considered is doing cash for keys, but I have not made up my mind hoping she will be out by the end of the month. Best of luck with your situation.

If they're on a month to month, can't you just say you have X days to vacate, where X is the number of days required by the state?  You shouldn't need an excuse to make them vacate.  Check local laws, but because it's a month to month, you're pretty much free to get them out whenever (given the proper written notice of course)

When you give them the 30 day notice, simply state "The owner wants possession".  There is nothing to go to court about.  It is your business and you are making a business decision. Still check your local housing laws to be in compliance, but that should be all you need. Best of luck!

@Katie Stone Dearest tenant ; We have elected to not to renew your lease endIng on such and such date . Please have all your items out of the home on such and such date . That is all Your friendly landlord