Source: Sauce McGavin
To teach Azumarill Belly Drum in Pokemon Scarlet and Violet, you first need to get the move with a different Pokemon. As we’ve explained in our separate Belly Drum Pokemon Scarlet and Violet, only three Pokemon can learn the move by leveling up: Iron Hands, Makuhita and Hariyama. Out of these three, only Hariyama and Makuhita are remotely viable here, because they obtain Belly Drum at levels 26 and 25, respectively. Why would you spend that much time grinding levels with Iron Hands until you get to 84? Anyway, once you have a Pokemon that has Belly Drum, the next step is to get yourself a Mirror Herb. You can purchase it at the Cascarrafa Delibird for thirty thousand Poke Dollars.
Now, in order to teach Azumarill the Belly Drum in Pokemon Scarlet and Violet, you need to remove every Pokemon from your party aside from ole Azu and the Pokemon that has the move. Also, make sure that the Pokemon that wants to learn Belly Drum has at least one empty move slot. Let Azumarill hold the Mirror Herb, and have a picnic with the two of them. That should do the trick. I mean, you can also go through the laborious process of carefully breeding Pokemon until you get an Azumarill with the desired move. However, I strongly recommend you go the Mirror Herb route instead, since it’s so much faster. There is literally no reason to waste time on breeding when you can just use one item and be done with it?