Is there a way to convert an old Atari 2600 so that I won't have to unplug my cable tv every...?

If you are asking if there is a way that you can plug a cable from the atari into the coax jack on the TV, in combination with the CATV coax, so you don't have to move the TV every time you switch from the game to the TV, then yes, there are manual and automatic switching devices available. you plug both inputs into the switch, and then plug the switch into the TV. with a manual switch, you just hit the switch to change between the two. with the automatic switch, as it implies, it works automatically.