Open a bank or credit union account for her, or give her parents money to open the account if parental signatures are needed. There are loads of other presents such as picture frames, birth cert holders, or you could be really practical and buy her clothes. Not necessarily clothes for a new born, you could get summer clothes now for a 1 year old which would do her next year.
I think the tree is a lovely idea...kids get so many toys nowdays and a lot of things like certificate holders etc just gather dust.
Would be nice for the child to grow with the tree....(if you know what I mean !)
I would love if someone had bought any of my kids a tree.......in fact I am thinking of getting them one each this christmas .....although I am sure they will look at me and go 'thats great mum but where are the toys!'
The tree is a great idea - Why not make it real with an annual outing to see the tree developing, so you're giving time to the child rather than money.