These are the heirs to Pedro II, of the House of Orleans-Braganza:
Isabel, daughter died in 1921
Pedro de Alcantra, son of Isabel died 1940
According to Wikipedia, Pedro de Alcantra, referenced above, renounced his claim in 1908 to embark in what was regarded in his mother's circles as an unsuitable marriage. The marriage was neither unsuitable or against the laws and customs of imperial Brazil. Its common for families of pretenders to thrones to engage in this sort of ridiculousness. This leads to a situation where there are two pretenders to the throne of Brazil. If the monarchy had not fallen, either the marriage or the renunciation would have been butterflied away. Wikipedia doesn't give much information about Pedro de Alcantra other than about the renunciation. Wikipedia discloses that most Brazilian law professors view the renunciation as invalid.
Pedro Gastao, son of Pedro de Alcantra, died 2007. Not much information on him.
Pedro Carlos, son of Pedro Gastao. He is a forest engineer and was interviewed by Michael Palin for his travel book and series on Brazil. He seems quite impressive.
The Petropolis branch of the family seems fairly liberal for aristocrats. If the monarchy survives into the twentieth century and gets more established, deposition by coup and restoration, Spanish style, is also a possibility. But historically the republic had at least one "hard coup", in 1964, and you can count a few "soft coups" like the one this year.