How likely is it that I can change a no-pet rule in my condo building?

I would really like to get a dog because I feel that it would help make me a happier person overall and to keep it from being euthanized.
Problem is that my condo building (out of the other 8 or so on the street) doesn’t allow pets. I’m not really sure where to start past asking the owner herself or going to and bringing it up at the next condo association meeting.
Does anyone have any success stories on the issue?
Thanks!
Google wasn’t very much help (or maybe my phrasing just sucked) hence why I ask here.