From the pics I've seen of 2010 rear axles(can't find 'em now though), they've got the same 1.5" block that the 08-09 model trucks have. I assume the same factory lowered torsion keys too.
I honestly don't see why a 31x10.50 wouldn't fit. They came stock on the older model trucks and those could fit a 33x10.50 with stock height.
You could check out this thread too....it covers why 08+ torsion bar trucks are so short. Search PreKey mod. It'll put the front of the truck back to 'normal' 4x4 height of 98-07 4x4's with the use of a 98-07 STOCK torsion key. If you do just the key, you'll get about 1.5-2" lift up front with the same adjustment bolt preload and the truck will be very level. After that, you can fit whatever can fit a 98-07 truck....32x11.50's with a small torsion crank.