What can I substitute for soda pop in a sweet pork recipe?
Apple juice is good with pork.  The frozen cans of concentrate are cheap and perfect for this use.
Apple juice lacks the dark notes of cola.  To get those I propose you add hoisin sauce.  It is very sweet, a great mix with pork (I have some boneless ribs soaking in some right now awaiting the grill) and will lend the apple juice more of a dark sweet tone. 
If you want to stay pure to your recipe, sub in one of the organic root beers on the market. They are easy to find and they will brag about how they don't do the stuff you dislike about Big Cola.  Whole Foods has a store brand one you could use.  Root beers vary a lot; try some first to make sure it has flavors you want for your pork.