I agree with the posters above. The days of airlines providing such attention these for so-called 'special events' (birthdays, honeymoons etc) are long gone in the main. Especially if it one is asking for themselves ...
Additionally, on such a short sector cabin are very busy and it would be difficult even if there was a will to do something.

Perhaps for a status passenger in a premium cabin it might possible on a medium/long haul flight. I recall flying in AKL back to BKK in 2006 on my actual birthday and was the only pax in the First cabin. I was treated very well, and even given a bottle of Dom to sneak out.

Sadly, there are many folks trying to scam something for free at every opportunity, and trying to appeal to the good nature of people with things like "oh, it's our honeymoon can we be upgraded?"

I think best to look for other ways to mark your birthday, especially if paying.