Really, we don't know the birthdays for most Oz characters. I guess this is pretty common for fictional universes, but if the Sanrio characters can all have established birthdays, why not the Ozites? Here are the only references I can remember as to when characters' birthdays occur:
- Based on two references in Road, Ozma's birthday falls on 21 August.
- John Dough was brought to life on the Fourth of July.
- According to Who's Who in Oz, the Chief Scarer of Scare City was born on Halloween (so I suppose I might as well wish a happy birthday to him as well), and Prince Forge John of Fire Island on the Fourth of July. I wonder if he and John Dough ever have combined birthday parties.
- Benny, the live statue from The Giant Horse of Oz, was brought to life sometime in May (which seems to be the default month for the Thompson Oz books to take place).
- The Cowardly Lion has a birthday party in The Enchanted Island of Oz, which is described as taking place in the summer, but before David Perry's summer vacation. I would probably guess late May or early June (neither technically summer, but close enough for all intents and purposes). This would mean that the Lion is not a Leo, but more likely a Gemini, which might account for his being both a coward AND a hero at the same time. Ozma, on the other hand, would be a Leo.
- Ojo was born on Friday the Thirteenth, but we don't know the month or the year.
- In The Forbidden Fountain of Oz, the Wizard of Oz reports that the Prince of Regalia (probably Randy, unless he's had a son, which is a distinct possibility) had a birthday party at the same time as the Emerald City's Clover Fair, "when the wild four-leaf clover was at its prime." This would likely place it in the spring, although I'm not sure there are any specific references to indicate this.
- In The Ozmapolitan of Oz, Tim celebrates his sixteenth birthday on the first of some month, but I don't think we're ever told which one.
There are other birthdays mentioned in the series, like Prince Pompadore's in Kabumpo in Oz, but I don't believe they're ever identified with a specific date, or even time of year. If I've forgotten any, though, please let me know.