It depends on the reason that management denied the permission. Is it noise from running on a treadmill? A solution to that could be to get an elliptical trainer or something similar.
I was looking for something more effective and interesting than a treadmill and found the Bowflex Max Trainers. They're neither treadmill nor elliptical, but kind of it's own breed of trainers. Apparently they help you burn 2.5 times as many calories as traditional treadmill or elliptical equipment. And, because you don't run or lift your feet of the device, there won't be any noise your neighbors or management can complain about.
I wrote a review on the Bowflex Max Trainers on my blog tomlikesbest.com to share what I found.
Maybe it's something for you.
To sum it up, I found that the Max Trainers are a really good alternative to treadmills. They help you burn much more calories and are better for your joints. Which one you get depends mostly on your budget. The M3 is a good tool, but the M7 is worth the extra money.