I just made a call to the gym to make sure when we can play badminton. Here is the answer:
1. there is no special time for badminton
2. We can't reserve the court
3. the only way is , in the available time( we can check the on-line schedule) if nobody play basketball or sth else in the gym, we just rent the poles and nets to play badminton. So difficult.
Suggestions: 1. try the existing way
2. write some emails or make some calls to complain and apply some special time for badminton , at least two hours one week .