In June 2012, the family history website Family Search added

Catholic Church Records for a number of States in Brazil, including Minas Gerais.  These records have not yet been transcribed, so you cannot search them by name.  Instead they comprise almost six million images of pages in the actual registers kept by each Church.  The records for Rincao all appear to be included amongst those for Bambui, so it is a slow process looking through hundreds of images searching for baptisms and marriages which took place in Rincao.  

Currently the following records are available on the family search website -

Baptisms - December 1918 to April 1951 (with some gaps and some duplication of dates)

Marriages - September 1882 to Feb 1952 (with some gaps)

In early June 2012, Family Search also added around 10.5 million Civil Registration Records for Brazil (1870 - 2009) - however, so far there are none for Minas Gerais.

Also in June 2012 they added Brazil  Immigration Cards covering 1900 - 1965 some of these include photographs and even fingerprints of the individuals as well as place and date of birth and names of parents.  These records are indexed, so it is very worthwhile looking for your ancestors.