I make this all the time for swmbo.. I even make the kool-aid part with Splenda so it's a diet soda
here's how I do it..
make kool-aid (make it a little extra sweet)
add to a 2 liter soda bottle
force carb it using a cabinator cap (30psi for a week in the fridge does nicely)
make sure to shake the piss out of the bottle to help get the CO2 into solution (I do this several times a day topping off the CO2 each time)