Cirebon is a coastal lowland city and hot year-round, with high humidity regardless of season. The dry season runs roughly April to October and is the more comfortable time to visit — lower chance of rain and slightly less oppressive humidity. The wet season (November to March) brings afternoon downpours and the occasional day when outdoor sightseeing is unpleasant.
Two periods are worth planning around. Eid al-Fitr (Lebaran) at the end of Ramadan sees massive domestic travel across Java; trains and buses are booked solid for days before and after, prices spike, and Cirebon's streets fill with returning residents. Unless you are visiting specifically for the celebration, avoid travelling through Cirebon at this time. Maulid — the Prophet's birthday — draws large pilgrimage crowds to the Gunung Jati tomb north of the city; the roads in that direction can be congested, but the atmosphere is festive rather than problematic for visitors.