Triggered abilities: Whenever a creature deals damage
Yes, you can do that. Each creature you control that deals damage to a player triggers the ability and puts another copy on the stack. Then after each triggered ability resolves, each player gets priority, so you can again tap your enchanted creature to put another token into play.

Note that you must choose the targets for each instance of the triggered ability when they are put on the stack. Importantly, this means that if the enchanted creature is destroyed in the middle of this process, then the rest of the untap abilities still on the stack fail to resolve, and you can't use them to tap or untap anything else.