It's . . . . . . . . pity that my birthday comes only once . . . . . . . . year.

In the first blank, article "a" will be used because here pity is being used in the general sense (a cause for regret or disappointments) and it is considered to be countable (general) noun.
In the second blank, article "a" will be used because 'year' is a common noun and has a consonant sound.