1) The closest tire size to your 31" would be 245/75R16. Very common truck tire size
2) I'm not sure on the 4WD, but on my 2WD '81 model, I had 265/75R16's with no issue. I currently have 285/75R16's (approx. 33") on my 95 Tahoe with no issues, but that's a totally different animal.
Casey
1995 K1500 Tahoe 2 door, 6.5LTD, 4L80E, NP241, 3.42's, 285/75R16 BFG K02's; 1997 506 block; Kennedy OPS harness, gauges, Quick Heat plugs, and TD-Max chip; Dtech FSD on FSD Cooler; vacuum pump deleted, HX35 turbo, Turbo Master, 3.5" Kennedy exhaust, F code intake; dual t/stats, HO water pump, Champion radiator; Racor fuel filter