Bearings jammed up even though there is play I've got a cheap new rear wheel. Disassembled the cones etc and replaced with my own grease. When trying to adjust the bearings to the correct tension, it gets to a point where the axle will make small movements smoothly, but will suddenly give a lot of resistance. If i turn the axle (not the cone), back to where it was smooth, there is still play in the axle, suggesting the axle should be rotating smoothly the entire 360 degrees. When I remove the cones, I usually see that one of the bearings has 'jumped' out of its position and on top of one of the others. What could be causing this? It's new so there's no pitting or corrosion. I think I used an acceptable amount of grease and there are 9 bearings each side.
You've given the cause in your first sentence.  I've got a cheap new rear wheel.

Cheap wheels tend to be not as good as better wheels.  So the bearing surfaces are not quite as exact in their tolerances as a more refined hub.
Is it possible that you have swapped the cones side-for-side ?

At these scales, its impossible to see visually whether its the cup or the cone which is out.

Lastly - did you change the bearings?  Are they the right size?  Are they all the same size?   You might be better to simply replace all the bearings with new ones, that way they're the same batch and thus size.

Rear wheel hubs should be 1/4" bearings (about 9), and front wheels are 3/16" (about 10)   I'm guessing you have loose ones, rather than those in a retainer.  Either is fine, loose ones are more fiddly but technically better. 

The bearings looking like they are on top of each other is probably happening as you unscrew the cone, not while its spinning.  There is simply not room for a whole bearing to jump another one, even when its got a lot of play.