If you are still reading this after the super-specific title, you must have some medium weight furniture to transport! The gist of it is that you're going to tie it to yourself, then jump on the bike. You'll want some thick rope, a bike, some furniture that you feel ok about tying to your back, and of course, you.
This works for just about anything you can carry on your back, and that won't hit the rear wheel. My gauge is if you can lift it above your head and sprint it's light furniture, if you can lift it above your head and run it's medium furniture, and if you can lift it above your head and walk, it's heavy furniture. If you can't lift it above your head, it's super heavy furniture (pianos and couches for example).
Step 1: Find the Furniture, and Add Rope.
What I needed was rope. Thankfully, I have a friend in that part of town who I knew had suitable rope, and would be home on a Saturday. So, I borrowed their rope, and set about making a a backpack out of an end table.
Step 2: Let's Get Knotty!
The primary knot I use here is the larks head, because it is fast, good around objects, and shouldn't bind. (it is also called the cow hitch) I think you can figure out how to tie it by looking at it.
You will need to make straps: I simply used one end of the larks head, stretched it out a few feet and then tied it to the bottom leg of the table. (Third picture is a good reference.) Try it on at this point, to make sure the loops are even, and that they are a good size. you want it to be like a snug backpack, but not so snug that you lose mobility.
Really, feel free to see what works the best for you. The end goal is simply to have a piece of furniture attached relatively comfortably to you, without hindering your ability to ride, and without it sliding all over the place.
Also, if you were already carrying a backpack, just lash it into place back there.
Step 3: Get on Your Bike and Ride!
Of course, you could get a trailer. But I think nifty improvised solutions are more valuable in many ways. Mostly in comedic and mental growth value. But it's also greener than calling a cab, or using a car.