Going to college in a few weeks on the other side of the country.
I have this 36" unicycle that I like to ride around, though, and the original box gave up the ghost awhile back. How do I get the thing from Alaska to Louisiana?
I think that the box that Coker sent me a wheel in was 37x37x9 which is pretty big.
You could just build up a box around it and send it to yourself, or if you are flying take it as checked baggage.
EDIT: if you bring it on a plane DO NOT mention the word “bike”. Say it is sports equipment and you won’t get charged a bike fee.
Just have your belongings shipped and ride your unicycle to the new location!
Alternately, make your own box. Tape, cardboard, a box cutter… this isn’t rocket science. The 36er can handle a UPD at speed, it should easily withstand some man-handling from the monkeys at the postal service.
FTFY. Sports equipment still rings some alarm bells. Circus equipment has worked for me a number of times.
Just be sure to completely deflate (even remove and fold) the tire. If they can feel a pneumatic tire in your case, they think bike, and slap on the charge.
If you are shipping in the US via UPS, make sure that the package dimensions are less than 36x36x9…or maybe 8. The shipping cost jumps a lot after that (check their site). I have done this a few times. As maestro8 says, deflate the tire. That gets the two longer dimensions down by at least an inch.
I have shipped a bare Coker wheel, with just a shipping tag attached. Cranks, no pedals, protects the axle ends. Bicycle shops are always getting rid of the boxes that bikes are shipped in. This gives you a couple of the corners already glued up stronger than you can tape them.
36" unicycles are tough to ship via UPS due to their size. Be careful of exceeding their size limitations! I think mine came by freight, rather than UPS, in its very large Coker box.
By all means try to keep the tire on for shipping if you can. Otherwise it’s a bare rim that may take the beating. However this makes the overall dimensions bigger, so if you’re boxing it and can put some good padding where needed, taking the tire off will work. I don’t recommend it in a soft bag. While the airline people can detect a tire, they can also detect a rim. It’s probably not a problem if they do, since it’s so big. Just say “What bike has a wheel that big?” Especially if there’s only one in there… 
You say you’ve got a few weeks - just ride it there 
Or put it in your car.
Something tells me he’s not going to drive his car 4,000 miles just to transport a unicycle.
Never now!
And then put your car in a box and mail it.