Hi Josie,
I go to the TG in Bornheim and they offer Badminton I think on Thursday nights, Saturday and Sunday.
It is a complete bargain at 9€ a month as you have not only badminton but all aerobics courses unlimited and other things as well. I think swimming is an extra 3€ a month though not sure the website will tell you more.
Also they are opening up a new leisure centre by the Panoramabad in September and I think they might be offering even more badminton then.
http://www.tgbornheim.de/Amanda