Diplomatic

Although President Monroe is making some big foreign policy claims (without a lot of military strength to back them up) he doesn't treat the European nations like enemies. He uses a fair amount of respectful language to show that he (and therefore the U.S.) sees them as authorities. Some of it could also be seen as a tad passive-aggressive, but it's hard to tell without hearing how he delivered it.

In the beginning, Monroe refers to the Russian leader as "His Imperial Majesty" (2). The U.S. is in the midst of trying to negotiate with Russia and convince them to give up some of the land they went ahead and claimed on the west coast. But the U.S. is all about "friendship" and its "great value," which can lead to the "best understanding" between the two governments (3). There's no angry ranting about Russian imperialism here.

Throughout the text, Monroe tempers his comments about Europe to make the U.S. look like a positive political force. For example:

The citizens of the United States cherish sentiments the most friendly in favor of the liberty and happiness of their fellow-men on that side of the Atlantic. (8)

America totally wants the best for those guys in Europe, really.

Even when talking about the most direct issues of the Monroe Doctrine, Monroe says:

[…] we could not view any interposition for the purpose of oppressing them, or controlling in any other manner their destiny, by any European power in any other light than as the manifestation of an unfriendly disposition toward the United States. (16).

That's a lot of extra words to say that interference in Latin America would be considered hostile to the U.S., which he does say in more aggressive terms elsewhere.

Phrases like "an unfriendly disposition," or "to preserve those relations by a frank, firm, and manly policy, meeting in all instances the just claims of every power, submitting to injuries from none," (21) take potentially hot topics and cool them down by maintaining dispassionate, diplomatic language that recognizes the power of Europe while also emphasizing America's determination.

Confident

The text is confident just by virtue of what it's trying to do. The new kid is making a speech to the popular crowd saying they won't let them mess with the even newer kids. Monroe didn't even have proper force to back up his points, so he's basically bluffing. However, when he makes his statements, he leaves no room to question his meaning.

Look at some of the main tenets of the Monroe Doctrine. First, we have "the American continents […] are henceforth not to be considered as subjects for future colonization by any European powers" (4).

He's not asking, he's telling.

Similarly: "we should consider any attempt on their part to extend their system to any portion of this hemisphere as dangerous to our peace and safety" (14). There's no wavering here. "Any" efforts will be seen as hostile, which means Monroe is telling these old, powerful nations that they can't make any moves in Latin America without risking retaliation.

Even at the end, Monroe clearly disses monarchical governments. Adding colonies to a monarchical system wouldn't just endanger the U.S. "nor can anyone believe that our southern brethren, if left to themselves, would adopt it of their own accord" (23). He's pretty much just telling Europe that no one would choose to be like them if given the option.

Bold move, sir.