Never, or at least- on no discernible date. Generally a nation becomes independent with support of an outside power and most of the time takes its system of government from its benefactor.

The Italian nationalists were homegrown but the kingdom of Savoy were one of their earliest supporters so their house was given the throne.

France during the revolution set up many client states with republican systems of government, but in the Imperial era set up client kingdoms with Bonapartists on the throne.

Greece was given independence by a domestic revolution, but only maintained as independent form external support as guarenteed at the Treaty of London in which the kingdoms of GB, France, and Russia insisted on a monarchy.

However there are many exceptions to this rule, and generally the area has to be taken on a state by state business. I think the only rule I'd hold to is that the creation of monarchies is much less common now because of the hegemony of democratic, or at least the illusion of democratic, systems of government.