Avatar is the guy from the movie "The Treasure of the Sierra Madre" who, in the movie say's, "badges, we don't need no stinking badges!"
If the ceiling height is a standard 8 foot (even if it's a tray ceiling as long as the walls are 8 foot) and there are no firebreaks in the wall this sould be a breeze. Pull the plate off the outlet your running the coax near. See which side of the outlet the stud is on and it's location relative to where you want the new outlet. If it is on the open side of the box and not the stud side you might be able to drop the new coax through the same hole in the wall's top plate as the e outlet's wiring, if the hole is large enough, if not then drill a new hole a few inches over. If the location for the new outlet is on the opposte side of the stud you'll need to meassure over about 6-8 inches from where the outlet's wring drops and drill a new hole. Meassure the height of the electrical outlet and cut a hole in the wall for the new coax using a low voltage box (a pop in backless outlet box available at most any hardware or home supply store for a $1 or so). The hole will be large enough for you to almost stick your hand in (you may actually be able to get your hand inside the wall) and will make fishing the wire pretty easy. Find something (I usually use a long drill bit that is smaller than the hole in the top plate and tape the coax to the bit (the bit is to give the end of the coax some weight, if the bit is the type with a small pin hole in the end, strip back the caox to the stinger wire and thread it through the hole in the bit, then tape around it). Drop the bit through the hole and feed in the coax until it goes slack, you should be able to raise and lower the bit a tad and hear it hit the bottom plate of the wall or the top of the electrical outlet box. Just reach in the hole (if your hand fits through) and grab the wire or use a wire coat hanger with a hooked end to catch the wire. Put and end on the coax, install the low voltage oultet box and the new outlet face plate. The whole operation should only take 10-15 minutes.
Now if your dealing with 9 foot or taller ceilings you'll need a flex bit (about $30 or more), more time and need to use more cuation so you don't damage the wall.