Best way to bring power to a moving garage door
You have two components which may be electrically isolated from each other if the door itself is not metal:  Tracks and spring/counterweight mechanism; and The opener track. You can make one positive and the other negative.  You will have trouble electrically separating the tracks and springs from each other. Keep in mind that spring preload is dangerous, cannot be reasoned with, and does not know pity or remorse or fear. 

However, I would be more inclined to use induction, or "two halves of a transformer".  Place one half on the door. Place the other half where the door is in the down location.  If you only need the lights to to work in that position, you are done.  Otherwise either a) have a second "transformer" primary in the open position; or b) install a large enough battery on the door. NiCd D-cells are a good choice, because it is not expensive and rides through abuse better than most.  A protected lithium might also do.   Presence or absence of AC would also be a means to detect door position. 

Keep in mind with transformers, the carried wattage decides the mass of copper, but the frequency decides the size of the iron core.