When writing thank you notes for things my daughter has received, I like to include her in the process. Now obviously, she's two -- so she isn't going to be doing any writing. But her contribution is usually some crayon scribbles, stickers, or a hand tracing.
Now, again -- she's two. This means that the balance of power has shifted a little bit, and if she doesn't want to do something... SHE DOESN'T! :) I'm sure no one else's child is like that, though... but since mine is, here's what I've started doing.
When my girl is in a coloring mood, I give her a couple blank note cards to scribble away on! That way, when I need to write a thank you note, and she's having a meltdown over the mere suggestion of coloring, I have two or three cards in my stash with her "signature" already on them. Why didn't I think of this earlier?!
This system works WITH her toddler independence, while allowing me to still send timely thank yous to those who deserve them. It's sort of a way to "strike while the iron's hot," if you will. If she wants to be coloring, she might as well color on a blank card. I just keep the colored cards (with their envelopes) in my desk where I keep other note card supplies, stamps, etc. When the day comes (and that's a "when," not an "if!") that she's refusing to cooperate, I'll pull one of these out, write a brief note, and stick it in the mail. No more "forging" your child's scribbles in a pinch!
Not that I've ever done that or anything.