For these carnitas, which means "little meats", I added a can of Coke to the crockpot while cooking. It helps to flavor and break down the meat.
In the past, I've also added another can of soda to the skillet when I seared the cooked pork bits to add some super sugary caramelization in addition to the searing.
You can try this with any soda. I've used Dr. Pepper before. You can use Pepsi. I think I remember mom using Cherry Coke with ham.
Use any soda with full sugar. You won't get the same effect with diet soda, for example. There's no sugar to caramelize.