Does anyone make a 37 inch MT for a 15 inch rim? 16 inch rim? Don't want 17 or anything bigger.

 

You can get a 37 toyo MT for a 15. Super swamper and pitbull also make 37s for a 15.

 

For 16's:
BFG KM2 - 345/75/16 or 365/75/16
Super Swamper M-16 - 37x13.5x16
Pitbull Rocker - 37/13.50/16 (Bias, didn't find a radial at the time I was looking)
Toyo MT - 385/70R16 (38/14.50/16 )
Falken Wildpeak/RockyMountain 325/80/16 (All Terrain)

I heard that the Maxxis Trepador has a 37/xx/16, but didn't find it anywhere.

And the Cooper SST was on my short list, but it was discontinued in the 16" size before I got around to buying.

I ended up with the falkens, about $100 less expensive per tire than the next cheapest.