Running cables under carpet. Any great methods?

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.