Everyone thought I was mean, but I kept asking for & finally they got it--$. Then go open up a custodial savings account for your girl. Every time you get a present check or green cash for your daughter, deposit it. As our girls have grown up, I would deposit their checks/cash & if there was something that they WANTED, not needed, we would talk it over & I would take them to buy that item. As they got older it has usually been clothes. One girl saved for a year & we bought her ipod. And although I never told them, I would really be using our $ for the item.
I really want them to have some $ for themselves when the time comes. And before we go out to buy their special present, we would talk about if they really NEEDED something, or just WANTED it? Because it was THEIR $ to spend & once it was gone, oh well. And 2 is not too early to start explaining that. One of my daughters, around 6 or 7 HAD to have some electronic Hello Kitty thing--HAD to have it, so & so had it, etc. She pooled her birthday $, I took her to buy it, she brought it home, used it for a day & came to me crying because it wasn't all that & a bag of chips! And she wanted her $ back. No way, Jose. Lesson learned. And she is the BEST saver, planner, $ spending decision maker of my girls now.
She's 15 & currently her account has WAY more $ in it than her older sister's, because she isn't as impulsive about wanting stuff. Older sister is hard on electronics & I've actually used some of her $ to pay for the replacement of broken ipods, netbook, laptop & over usage of cell data.
IF family/friends HAVE to bring a gift, because they want to see her open up the packages, make a list of crafts, books, crayons, that sort of thing that will be used for a while, but aren't too expensive. But send/bring bulk of the present in $. Is this crass? Yeah, probably. BUT if you explain to family/close friends your strategy, most understand it. And this way everyone gets the joy of the gift opening.
And in 15 years or so, your daughter will have a nice little nest egg ready to buy a car, rent an apartment, college expenses, etc.
My girls get it, especially now, when they see that all of their life gifts are in the CR waiting for them to use responsibly. Or not. And that they have been given & then passed on to friends or Goodwill many, many more gifts, so many that they can't even remember them. The $, they remember! And are grateful for! Good Luck.