Which is correct sentence?

Hi Victoria,

Perhaps we can start with some basic concept of the word "is".

"is" is an example of linking verbs. Linking verbs are used to describe the state of a noun. 

As an example: "He feels bad." Notice that "feels" does not function as an action word here; instead, it functions to describe a state (emotion). Hence, "bad" (an adjective) is used to describe the person. We will not write: "He feels badly." simply because "badly" (an adverb) is not used to describe the person. 

Sentence 1 sounds a little odd to me, as you are not using "May 9" to describe the state of your birthday. 

We need a preposition to show a relationship between two nearby words. In this case, we use "on" to indicate the time when your birthday occurs. Hence, sentence 2 will be more grammatically correct.

Hope this helps.
Cheers, 
Lance