The timing of your visit to Michoacán depends almost entirely on what you want to see.
For the monarch butterflies: November through March. Peak numbers are typically in January and February; the butterflies begin to disperse back north in early March. Visiting in December or January gives the best chance of seeing the largest clusters.
For Day of the Dead: Late October and early November. Pátzcuaro and the lake island of Janitzio are among the most celebrated places in Mexico to witness these observances, drawing visitors from across the country. Book accommodation months in advance.
For general travel: October–April is the dry season on the central plateau, with mild temperatures and clear days. May is the hottest month before the rains. June through September brings afternoon thunderstorms that are usually brief but intense at altitude.
The Pacific coast is hot and humid year-round; February through May is the driest period down there.