The United States president James Monroe declared that no European power was to establish any new colonies or puppet kings in the Americas following December 1823. Is this something that the United States realistically could have enforced? The War of 1812 resulted in the US military suffering numerous defeats, and American industry at this time was not on par with that of the European powers like the UK and France (from what I remember hearing about American industry in the 1820s). How did a country that was shown to be militarily and industrially inferior manage to secure the Americas from European involvement?
Something important to consider is the fact it was Britain who was largely interested in enforcing the ideas of the Monroe Doctrine, particularly against potential Spanish revanchism (not that Spain had the will nor the means to to pursue such a policy realistically). The United Kingdom was deeply committed to a policy of free trade across the world, largely to fuel the burgeoning industrial development of the nation. Free access to the cash crops of Latin America was important, as was access to their markets, aims that could not be achieved if any European state re-established colonial control. As such, we see a committed British effort to prevent potential Spanish resurgence in the early years of the nineteenth century, which was obviously helped by the dominant position of the royal navy post 1815.
A quick note on the idea of puppet governments in the Americas though: gunboat diplomacy and economic influence meant that these new states still found themselves with often unequal ties to more dominant powers. First these were European nations, then increasingly from the USA as the century progressed.