If you can save up about $40, you can get a good binder from Love Boat. The packages do say Love Boat on them, but nothing LGBT related or anything. Buy a Visa gift card and buy it with that. If you have to send it to your house, pay attention to the tracking info (erase internet history!!!) and know when it will get there, so you can get to the door before anyone else. You'll probably have to sign for it though, so have some excuses ready. This worked for me, because my parents don't pry too much; they trust me, and I normally get things from eBay and Amazon every once in awhile, so it's not unusual. If you can't accept it at your house, get a good friend to do it for you. The T-shirt excuse Jacob suggested sounds like it would work.
If there's no way to get a real binder, use an abdominal binder. You can buy them at K-mart or wherever. Good luck!
@Bagheera - If you meant discrete; Underworks ships under the name Simple Solutions.