One of the Trainer Tips in Magikarp Jump says something to the effect of, "Once your berries are upgraded to a certain point, you may get support candies". I noticed that at level 25 you get one support candy upon the 25th upgrade, but the tip suggested to me that you might get them at random or through some other mechanism; and further, the large numbers needed for various things suggest to me that there must be a better way than just getting a small number when winning certain league matches or the relatively rare upgrading a candy/training to 25 (which is very expensive). I've played up through level 20 Magikarp (trainer level 10) and have only seen three support candies total.
I'm looking for a better way to get support candies, or a sense for how many you'll ever get. So:
What is the list of ways to get support candies?