I'm under the impression that this is very doable...
You're looking for a 'kegging' system (NOT a 'Kegerator', which has a refrigeration mechanism), often used by homebrewers to carbonate beer, wine or mead...rather than the more tricky and time-consuming process of in-bottle carbonation. (Can anyone say 'glass grenades'?)
Check websites and local retailers that sell supplies to homebrewers..IIRC, they run in the $300 range for the basics (valves, regulators and gauges), plus soda kegs and CO2. I don't know what soda kegs with syrup would cost, but call your local beverage distributor. Or, buy a couple used soda kegs, find a recipe for something you like (you'd be surprised) and put up your own...run through the kegging system it'll be a fizzy as store-bought.
You can run the tab up quick, however, if you start spending on fancy-schmancy taps, multi-line systems, etc...so be careful.
If you get that far, and also want chilled beverage, let me know. There is a cheaper way than a kegerator...
Good Luck!