Just FYI, I experimented a bit lately with a mini-keg for carbing soda (a 3 or 5 gal corny would be the same idea, and provide more volume). This should work if your tap water is good enough for soda.
This was super-simple - I half-filled the minikeg with tap water (and set it on its side to provide max surface area), applied 30PSI CO2 and set the minikeg in the fridge. It carbed fast with all that surface area, plus you can shake to speed it up.
For a more-less continuous supply of soda, 'tee' your tap water supply into the dispense line with a valve to control water flow. When you tap a serving, open the water valve to replenish the supply of water. Since your main water pressure is higher than the 30PSI carb level, the water will flow in, and further compress the CO2 in the head-space.
Since you are just adding a small amount of water at a time, the temperature and carb levels don't drop much, and it seems to fully carb back up in a short time. Of course, if you are drawing off large amounts (relative to your keg size), it will get relatively flat and warm. But it's simple, no separate carbonator pumps or anything. And you have very efficient use of your CO2, since you are not venting off any pressure to open and fill - the water enters under pressure.
I did this with a very manual set-up, just to test it out. I just monitored the pressure as I added the tap water, and either let it get up to ~ 40PSI, or I'd judge by the weight of the keg if it was near full. The higher pressure after filling helps to speed the re-carb process, and drops down as it is absorbed.
I might hook up some check valves and regulators to make this more automatic next summer, when we use more soda water.
-kenc