Yes, I am a december baby. It's fairly shit
everyone's saving up for christmas, plus they think you'll be ok with the one gift.
As a child - you're not! 
Since you cannot possibly demand 2 gifts without looking bloody rude, might I suggest the following totally PA manipulation. 
Phase 1
Ask them if they are going to use birthday wrapping paper or christmas wrapping paper.
Ask them if they would prefer her to open her gift from them on her birthday or on christmas morning.
That should get them thinking. 
Phase two.
Start asking people if they would mind if you rewrapped their gift in fancy birthday paper (if they used xmas paper) / xmas paper (if they used birthday paper), because you want her to have a birthday too, like everyone else, so you are dividing gifts into birthday and christmas, so she has something to open on both days.
If they don't get it after that, there's no hope 
It really isn't about the value of a gift, hell it can be a packet of plasticine from the bloody pound shop! It is about someone having their birthday and it not being taken over by christmas.
My parents always used to put up the christmas decs on my birthday. Apparently, this made my birthday 'special' 
I promise you that it did not.