I have 2 ideas for you to consider:
Last year, my sister donated a flock of chickens or something like that, in our name to a charity that helps the poor in 3rd world countries. I thought that was pretty cool. Now we get a catalog, and there are lots of choices. Heifer.org will even send you a little gift notification card, that you can present to your family member. You can donate sheep, goats, llamas, ducks, pigs, cows, chickens... We will be doing that for my sister this year, since she has shown that this is a charity she cares about.
Toys for Tots is a charity that donates toys to needy children. They are delivered by the US Marines on Christmas Eve.
A quick search online, will give you many results for charities that need money during the holidays (and all year). You could tell your family members (adults) that you will be donating to charity in their name, and suggest that you would like them to do the same. It could be fun to see what everyone comes up with... exchange greeting cards with a note inside, explaining the gift that was given in your family member's name.