There are a few simple things you can do for badminton training that you might find useful;
12 cones in a circle to represent numbers on a clock face. Call out three numbers and the player runs to those cones always facing forwards (so 12, 6, 3) would be forwards, backwards, right (for the player). Then reverse it, then make the player call the numbers...works not only the agility side of playing, but also on 'dexterity of the mind' (I wrote that as I can't think of a clever name for it)...
For the next one you'll need shuttles, lots of them, 2 colouring in pens and a player...Colour some of the shuttle ends one colour, some another and some with no colour (make the colours easy to see like black and red). Stand a few feet away from the player and throw the shuttles. Any shuttle thrown to the player that is black they need to use a forehand swing (without racket), any red is a back hand and anything not coloured they leave.
Stand on the other line with player on the inside of the tramline (can be done anywhere), bounce a tennis ball left of right. the player needs to recover the tennis ball (by catching and sympathetically throwing it back to you) before the ball bounces for a second time. They can only use the lunge technique to do it. So they will be lunging left and right to recover the balls.
8 cones (or markers of any description). Set up two cones to your left and two to your right. Place one of the cones about 1 foot in front of you and the other 1 foot behind you and set the same up for the player who will be standing in front of you. They have to mirror your movement. So if you go left, they go left, if you touch the rear cone they touch the rear cone. When they get good at this opposite it. So if you go right, they go left.
4 pretty simple exercises that don't involve getting a court or going to a gym, but use the movements and decision making of badminton.
Basically anything that makes your player go the wrong way and have to correct themselves us good, anything that involves them having to use their brain and anything that is sympathetic to the movement involved in the sport (lunges for example).
I'll not take credit for the activities though. Credit goes to Andy Allford - GB olympic badminton coach (and a pain in a arse to follow on the last cone exercise)...
*Edit* - With regards to being sympathetic to the movements an example would be - Why not try lunging for a shuttle while someone has a resistance band wrapped round your waist...