To come back on topic: the only way to re-instate a monarchy is going the Franco way. That means: a strong man who decides that it is in the country's interest to have a (purely ceremonial - he does not want to loose power, of course) royal head of state from "the historic dynasty" which has to be the embodiment of the country's new-found self-consciousness, pride and glory.
Well, that means "strong men" as a Vladimir Putin, as a Viktor Orbán, as a Recep Tayyip Erdogan, who propose the Parliament -which often acts like puppets to their puppet master- to restore the Russian, the Hungarian or the Turkish royal families into a "Sweden-style" monarchy.
Other than this "strong man scenario" I see no any possibility to let republics turn into monarchies again. The case of Greece, where a state has so utterly failed as no any other European state in recent history, where the people are so confronted with the toughest and most draconic austerity measures, even there no any call was made to send the utter failures home and bring back "the good old days" (well... they were not thát good, but okay). When even in such a situation, a nation shaking on its foundations and on the brink of total collapse, there is no any desire for the monarchy as an alternative to the arch-corrupt, nepotist, disfunctional constitiution, then there is no hope for old royal families to be restored again.
The only possible way is an "enforcement", for an example by an alliance of Putin, the Orthodox Church, the elite, the armed forces. In fact similar to Franco, backed by the elite, the Catholic Church and the armed forces enforcing that Don Juan Carlos de Borbón y Borbón would be his successor as head of state, as King of Spain.