My solution for you it to buy a pair of wheelbarrow wheels at Harbor Freight, Northern Tool, or similar store. Take off the bottom 2x4 off of one of the short ends, where the 4x4's touch the ground.
Take the wheels into Home Depot or Lowes and find steel bar stock of the correct length so that you can drill a hole through both 4x4's on the end you altered and make an axle. Looks like a 5' piece should do. Get 6 large fender/flat washers of the same inner diameter.
Jack up the altered end, put it on blocks. Drill your axle holes in the 4x4 post down low enough that with the end jacked up the wheelbarrow wheels are just off the ground. Fit the axle so you have 2" outside of the 4x4's on either end. Drill a hole thrugh the steel bar 1" from both ends that is just larger than a heeded nail. You'll need 6 nails total.
Thread the axle through one side (4x4), place a fender washer on the outside and place a nail in the hole you drilled, bend the nail in a circle. This keeps the end washer on place. Thread on in this order in between the two 4x4 posts, washer, wheel, washer, washer, wheel, washer, and thread the axle through the other hole in the other 4x4. Add the other end washer and bend the nail in a circle. Your axle is now captive.
Drill a hole in the steel bar 2" from the inboard side of each 4x4 post. Put a nail in the hole and bend in a circle, slide over the washer, the wheel, and one of the two center washers. Drill a hole 1/2" from the inner washer, place a nail in the hole and bend it. One wheel secure in place. Repeat on the other side. Two wheels secured. That 2x4 you removed in step 1, attach it as bracing between the two 4x4's a few inches above the top of the wheel.
Get 2 10' 2x6's, and attach to the sided pointing to the other end of the coop. 5' attached, and 5' as levers. Use at least 10 3" screws per side. More is better.
Insert a jack, raise the end, remove the blocks, lower the jack, grab the lever, move the coop. You may want to support the axle inboard of each wheel about 2" so the axle doesn't bend too much.
Just an idea I was contemplating should I need to move my coop.