I was a student myself recently, there's probably a few good ways to get in contact. I would say now is the best time to be marketing obviously as many students are leaving, but one popular thing that used to happen at my halls all the time is people would wait outside until someone just let them in, then post flyers under the doors of the flats. It probably sounds a bit sketchy but we used to get it a few times a week without fail, usually club leaflets.
You can contact accommodation providers as well, where I was, there was an advertising notice boards on every level on the stairwell where people can put adverts, so maybe ask to pin something up there?
Personally I doubt the student unions will give you much time, so I would say target the accommodation providers, most accommodation is run by private companies, even the official uni ones so I would contact them. Maybe say hey if you let me pin flyers your students can have 10% off etc.