The Heifer project is indeed pretty cool.
I also know some animal rescue or rehabilitation organizations offer an “adoption” program. That is, with your donation you (or someone you specify) is sort of a foster parent to that animal. I’ve done this with a bat conservation society for several people. They get a little packet with a picture of “their” bat and his name. And a certificate. Stuff like that. It makes it really “gifty” which I like.