In issue 171 of Driving Digest, I wrote about what makes a good or bad reinback.  I gave a great exercise in that article on how to teach your horse to reinback.  Here are a number of tips and tricks that will also be helpful in your reinback.

Many times your decision to reinback comes off as completely arbitrary to your horse.  As far as your horse knows, the two of you are standing in the middle of ring somewhere, you decide, "hey let's go backwards where you can't see anything."  Your horse doesn't think you're all that bright to begin with, this only furthers that opinion, especially if he's not comfortable with backing up.
I generally stop in the same area at the end of a drive before I unhitch.  In my barn yard I unhitch about 10 feet to one side of the barn door.  The horse can see the door as we are unhitching, and of course once unhitched we walk forward and away from the unhitching area, and into that barn door. 
After a drive, the horse is mainly interested in getting unhitched, so he's a pretty willing participant to do what ever it takes to make that happen.  When it comes time to start discussing the reinback with a horse, I'll "overshoot" the unhitching spot.  I'll stop with the horse about shoulder beyond the door, so the door is behind the blinders.  At this point it makes perfect sense why we are backing up; because we're not in the unhitching area.  So he's willing to take the few steps backwards to help you get him unhitched. 
In time, I'm able to make the reinback a condition of getting unhitched.  Soon enough, I am "parking" the carriage each time.
If just going past the unhitching are isn't a compelling enough reason for the horse to willingly reinback, I can usually find a more convincing reason to go backwards.  There is a large, concrete manure pit at the barn where I drive.  It is basically a three sided foundation on the level with the ground that we can drive right into.   
I usually will drive into the area about the length of our turnout, halt and stand for a moment or two.  Then, using all of the same physical and verbal commands I would like to use to create a reinback, I ask the horse to reinback.  While there is enough room for a clever horse to turn around in the space provided, most are quite happy to back up at least a few steps to get out of there.  In this case, it makes perfect sense to the horse.  Since the walls are about 8 feet high, the horse can see that there is no reasonable way out, other than the way we came.
If you are not confident in your horse's ability to remain calm in that situation, a fence or a wall will often work as a starter.  Of course, using a one dimensional wall usually allows the horse to step sideways after only a stride or two a backing up, but it's a start.

Even though I use a carriage shed that doesn't allow me put the carriage away with the horse still hitched to it, I still make the horse "park" the carriage.  Mainly, this is a matter of deciding a specific spot that I'll want the carriage to be before I'll unhitch.  If this is a new exercise to you, I'd encourage you to use cones, or limestone to mark out a parking spot.  Marking the parking spot is more to get you to communicate more effectively than it is to illustrate to the horse where the carriage will be parked.
When you are parking the carriage, look at the parking spot in relation to the carriage, and focus primarily on getting the carriage into the spot, rather than moving the horse.  The more you focus on parking the carriage, the better you will direct your horse what you need.  
Start off with modest goals.  Halt directly in front of the parking space.  Get good at backing the carriage into the parking spot over the distance of just one carriage length.  As you and your horse get good at this, start from a little further away, or off center.  When you are really getting good, stop at a 90 degree angle to the spot, then back into it.
Don't forget to use your whip to help guide your horse left and right, and really calm, clear verbal commands.  I use the words "left" and "right", plus the reins and whip.  Remember, don't just pull on the reins the whole time.  Be light and communicative with the reins!

When your horse is good at the reinback in the yard, you can apply what you've learned in the ring.  Your horse will have a good deal more confidence, and should be willing to push the carriage back without any trouble.
You're going to have to take most of the responsibility backing up straight.  This means starting straight.  If your horse stops crooked, he'll most likely back up crooked.  So you'll have to work on getting straight into the halt.  This is usually best accomplished from the walk.
It's best to switch your reins into your left hand, either in the coachman's position, or the Hungarian position.  Then, use your right hand to use both reins together to evenly request for the reinback.  Using the reins with two hands to request for the reinback will frequently lead to asking more on one side than the other. 
Take advantage of what you learned about backing up your carriage, rather than your horse when putting the carriage in a parking spot in the yard.  Look behind you for a moment, and decide upon a specific place to back your carriage to.

DO:
Take your time
Collect your reins in your left hand, and use your right hand to request the reinback
Take your time
Use a clear, unique verbal back command
Take your time
Give a release as soon as the horse begins to reinback
Take your time
Look over your shoulder, and choose something specific to back your carriage up to
Did I mention to take your time?
Use your whip to guide your horse straight backwards

Don't:
Rush the movement trying to get the horse go all backwards right away
Ask your horse to back up before establishing an immobile halt
Pull back on the horse through the whole movement
Try to get a 5 meter reinback before you've been able to get a single step of reinback
Punish the horse for not going backwards
Watch the horse to see if you are going straight backwards (watch where your are trying direct the carriage instead)
Make larger than necessary rein movements to correct crookedness
Use different verbal cues to reinback from one day to the next

As with every other area of training, practice and patience is the key.  This won't come to you in one or two workouts.  Keep your expectations modest, and build upon one small success after another.  The reinback that you'll create over time will be clear, controlled and confident.