Running cables under carpet. Any great methods?

The best method is the go under and bring it back up on the otherside. This means dril holes in the floor. So it would have to be your own propery. And that you could do it. That is pretty much the standard best solution. You can get small utility devices to cover the holes and be a block to insects etc. If you have no real foundation under the place. If you have a basement it is THEway to go.
As for under carpet, AND you do not wantt to have to lift the carpet to place it.. whoooh. Gonna be tough. You might try a wireless system to avoid the wires at all.

If you can lift the two locations of entry and exit of the carpet without causing damage. Rent or borrow an electricians fish tape or better yet the fiberglass stiff fish rods to push a string through the pull the cable back through. But make sure it is not in a traffic area as repeated crushing from foot steps will eventually damage the cable and cause a short. If the new location is not crossing a traffic area, e.g. hallway, adjacent room etc., you may consider tucking the cable under the baseboard trim, I have found that a coax can usually fit in that space.

Actually using a router to cut a channel in the wood baseboard in a hidden area, (of course this means removing them. cutting installing and replacing), even around doors could be a better solution, it just means the wires are longer...