It could be that the name of the birthday is Marine Corps Birthday, but if it is that the Corps, as a unit, owns the birthday, it seems it should have the possessive apostrophe, 'The Corps' Birthday is November 10th.' However, I can find no example of this in anything written about the Corps Birthday on the Internet, and I have to defer to Batman. On his show, I watched at the same bat time, same bat place as a kid, he was a stickler for the King's English.
-Will