From Wikipedia...
Elias Calles was president in the period 1924-1928, but in the next six years, there were three presidents, all of them subordinate to a lesser or greater extent to Calles.
Emilio Portes Gil (1928-1930), was designated by Congress to replace the president-elect Álvaro Obregón, assassinated before taking office.
Pascual Ortiz Rubio (1930-1932), elected to complete the term but resigned.
Abelardo L. Rodríguez (1932-1934), was designated by Congress to substitute to Ortiz Rubio.
The influence of former President ended when Lázaro Cárdenas del Río expelled him from the country in 1936.
Calles actually assented to Cárdenas when the PNR (today's PRI) picked Cárdenas after rejected in Calles's pick in 1934 with the assumption that he could control him. In actuality, within two years Cárdenas had managed to get rid of all of Calles's supporters among the State Governors and even Calles himself.
So how do we get another pick from the PNR to go into the General Election? Mexico at that point was a one party state so anyone that that was picked would have been elected.
There are several possiblities that would be loads of fun including Gen Nicolás Rodríguez Carrasco (the founder of the Fascist Gold Shirts), Aarón Sáenz Garza and Luis Napoleón Morones.