The Search for New Neighbors

Dear Apartment Guru,

I live in a four-unit brownstone and my upstairs neighbors are getting ready to move out. I love them. Our dogs play together and they are perfect neighbors. My problem is, my dog hates cats so I am hoping whoever moves in doesn't have a cat. Also, I REALLY don't want young kids moving in up there because we share a backyard and it could get noisy with running back and forth upstairs. Now, I don't think I have much say in who we can get to move in there. But is there any way or anything I can say to my management company to help influence them with their decision about who moves in? If so, what can I do?

-- Discerning, Not Discriminating