From what others have said they do eat random food and so far the list consists of, rare flower, rare mushroom, raw prime fish meat, raw prime meat , Sap , leech blood, and organic polymer. Make sure to have a decent amount of each one of these before starting the tame.
Taming these wont be able to knock them to unsconcious level, however they are tamed using recommended berries that shown on the upper corner, once you have the berry that he want, put it in your hotbar and give that fat moochops the berries. There is time to wait they hungry again.
For anyone thinking that you have to knock these guys out, no that is the WRONG way to tame them as they will not give you your inventory. This is because when you try to knock them out (i.e. punching/hitting them) their default reaction is the same as that of a parasaur - to view it as a threat, and immediately run away in fear. The way you tame these guys is simple. You feed them any berries found in the bushes (not including stimberries or narcoberries), and then follow them around until they get hungry again. Parasaurs are also herbivores, much like moschops, but parasaurs need to have a bola thrown at them first, especially for new players as they will most likely outrun those guys, but because Bolas deal damage and Moschops will view any form of damage caused intentionally as a threat, and run away fearfully, the exact same fear that will prevent you from taming them. Long story short, you have to be GENTLE when taming moschops, not knock them out like half of every other Dino...
If you can’t find any look for the red obelisk follow the rocks the the south east part of the isleland and you’ll see two giant rocks leaning on each other just search on both beaches and look a bit inside the forest.