I want to drop a small safe between the floor joists, and conceal the whole thing under the carpet. Ideally it would come with a flat cover, or I would can make one.  Problem is, all the floor safes i've looked at seem to be designed to be set in concrete, there seem to be very little offerings specifically for wooden floors.

Basically, I need something like that, but more substantial, with a thicker door and body and a combo lock:  http://www.deansafe.com/stsaqkrvsaor.html

can someone steer me in the right direction?

http://www.amsecusa.com/floor-safes/brute/

Up to 16x36 inches in size.

Electronic lock.

Thicker steel.

For less money, Home Depot's website has sub-par ones for $133 ones with no-name electronic locks and thin steel.

Most real safe companies will have the ability to fabricate whatever mounting solution is required for your purposes.  I have installed regular floor safes in concrete floors, wood floors, wall, motorhomes, boats, etc.

A competent installer can make a floor safe install in a wood floor perfectly secure. The simple solutions include placing the safe next to a joist, and running big lag bolts into the joist from the inside to anchor it securely. Installing a few 2x4 blocks inside around the opening to frame the cut in the floor adds strength and support for the floor cutout. Some contractors build a plywood box in a floor cutout large enough to install the floor safe in a concrete pocket just like you would in a slab install. That provides a degree of fire resistance too, as well as a strong install.