I am building a new house and am looking for an AC ducting system for use with a regular AC (only) unit, but that doesn't use the large flexible duct system. I know there is rigid ducting out there, but don't know where to start looking. Also can you use the 2" ducting for a regular AC unit?

If your thinking of using a system such as a large wall type unit instead of a central type system where the fan is in attic or in heater and the condensing unit is located outside and connected with pipes. Ducting this type of unit will not work. The fan is simply not strong enough to deliver the air out the ducts.
They do make a unit however that looks like a wall system that is typically placed in an attic with its end flush with the outside wall. A grill covers this. This Packaged Unit as its called is designed for use with ducts.

If you still want to attempt this however what your looking for is Duct Board. It typically comes in one inch thick five foot by 10 foot sheets. Special cutters put V groves in the board and its folded into a box shape. A special staple gun that flares out the staples is used to hold the edge flap down then the use of Metal faced foil tape is used to seal the seam.

Below is a link for this stuff.
You will still need flex duct to connect to the ceiling grills However.

http://www.specjm.com/commercial/airhandling/ductboard.asp

To answer your 2nd question about using 2" flex duct. All sizes of flex duct can be used. However as the duct gets smaller the air friction gets higher which puts a bigger load on the fan. Add to that the air flow speed increases the smaller the ducts are. The noise that the duct also makes is higher the smaller the size. Do not forget that if you use 2" flex duct it needs to be insulated so it does not sweat. The insulation needs a foil vapor barrier on the outside to prevent condensation issues.
If space is the concern look into Space Pac AC system made my Hydrotherm. Google it and you will find out all about this mini ac system that does use 2" ducts/