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.
cooking.stackexchange.com/users/53826/Willk
The main function that soda adds in these recipes is as a flavored syrup that also has an acid.
So make your own.
Add your preferred sweetener to water with some form of acidulation (I prefer apple cider vinegar with pork) and a few spices and you will have something suitable to use.
cooking.stackexchange.com/users/65929/AGirlHasNoName
I learned a recipe for a chicken dish from my mother.
Her recipe also called for cola to create a sticky and caramelised sauce.
She taught me, however, that the cola could be replaced with fruit juice.
Her preference was a mix of pineapple, mango, and orange juice.
Shops where I live call this juice mix "tropical fruit" juice.
It stands to reason, though, that any of the above juices individually, and maybe others, will work, too.
Here's an example of a recipe similar to what my mother taught me, supporting my claim of the juice helping to create the property sought by your question
cooking.stackexchange.com/users/73238/ant
What about something like Hansen's ?
It's available at the local store here in Nowheresville,
MN population
~7k
so it shouldn't be too hard to find.
cooking.stackexchange.com/users/73250/spock74
The flavors in Coke are cinnamon, vanilla, and citrus.
I personally taste cinnamon the most.
Dr. Pepper has a lot of other spice and berry flavors, and is similar to root beer.
You could try to recreate the cola taste by using apple cider vinegar and adding cinnamon, vanilla, and molasses.
cooking.stackexchange.com/users/72182/jreese
Depending on how much time you have, how often you would like to use this (or similar) recipes, how much you like the idea(s), and how involved you want to get...
you could try making a cola syrup recipe*.
You could even reconstitute it with club soda, or carbonated or sparkling water, or use water, a sprinkle of yeast, and some time to turn your syrup into a cola you can directly sub into the recipe.
This does require a much higher up-front investment, but it might be fun on one hand, and work for other recipes (and, yanno, drinking sodas) on the other.
*example link was randomly chosen
cooking.stackexchange.com/users/47365/Megha
I was looking up sweet pork recipes and every one of them call for Coke or Dr. Pepper.   I avoid soda as much as possible because of questionable ingredients: specifically GMO corn syrup, sodium benzoate and caramel color.  Are there any safer substitutions I could use to achieve the same/similar flavor?
What can I substitute for soda pop in a sweet pork recipe?
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<meat><pork><soda>
cooking.stackexchange.com/questions/96690
cooking.stackexchange.com/users/73234/Dianna Houx
You can try making a cola syrup or substitute with fruit juice, root beer, apple cider vinegar of a mixture of apple cider vinegar, cinnamon, vanilla, and molasses. Alternatives to cola include fruit juices and root beer. It is also considered while making a recipe of your own with sweetener, apple cider vinegar and cinnamon.
Fruit juices are a good substitute for cola in cooking. Root beer is a natural substitute for cola in cooking. Try to recreate a similar taste to cola with a recipe of your own, using, for example, sweetener, vinegar and cinnamon