Not an action
The way I have seen it played with Charm Person (to which Charm Monster is identical), an opposed Charisma check is either done in addition to whatever other checks and actions required (e.g. using Diplomacy) or is not an action at all.
In most cases, this is a limitation that makes the spell quite a bit weaker than the much-feared art of Diplomancy, so it's just an additional check you have to make to succeed at something else. You gain something (an automatically friendly attitude) for losing something (having to make an extra check)
However, because no special action is specified for an opposed Charisma check, it is itself no action at all, which enables you to make it when it's not your turn (which you usually can't do with actions).
Take note that while speaking is a Free action that you can even take on someone else's turn, "treat the target’s attitude as friendly" means that you have to use Diplomacy to Make a Request, which "takes 1 or more rounds of interaction, depending upon the complexity of the request". Improving target's attitude further would take 1 additional minute of talking.