80W90 is quite widely used, but I've noticed that it gets pretty thin here in July/August. Especially when the mower is parked and the tranny cooks in the brutal sunshine. If your part of OK is hotter than my part of KY, you might want to consider 85W140. I'm going to top mine up with 140W in the spring.
Unless you own a old worn out one like mine that likes to leak everywhere. I filled mine a couple of years ago with a NGLI# 00 rotary mower grease, same stuff I use in the old snow blower gear box. Not a leak since.
If yours isn't a old antique rattle trap like mine a 80 to 140 weight gear oil (depending on operating temps) should be fine. Personally I would probably go with a multiviscosity 85W/140 like Greg suggested.
Thanks for the responses. It is very old, but doesn't seem to be leaking at all. I have read some discussion of using grease, but I didn't know if it was good for general practice or just for old mowers with leaks. And I didn't know if there might be some brand new whiz bang high tech lube that I had missed out on.
I use NGLI# 00 grease in alot of equipment I have that has old gear box's. It's not like the grease in your grease gun. 00 grease is a semi-fluid and is not solid like you would think of with a NGLI# 2 grease. It's almost more like a heavy/thick gear oil, one reason it's great at stopping leaks.
If you want that brand new whiz bang high tech lube kinda feeling you can get a tube of STP gear lube additve which is very high in ZDP content. Has lots of EP (Extreme Pressure) and AW (anti Wear) properties. $3 a tube at auto parts stores.