A friend who is a French teacher re-uses Christmas cards in her classroom.... the kids cut off the front, glue it to a sheet of construction paper, and write messages in French in the inside. It's good practice for French holiday vocabulary, and a fun project. She also collects multi-faith cards and generic scenery cards, naturally, so non-Christian kids can make other sorts of cards.
She has NO PROBLEM finding donations! Even the most sentimental people don't usually need to hang on to the cards that, say, the dentist's office invariably sends.
It's possible that there's a teacher near you who does something like this; most everyone knows SOMEONE who teaches school, ask them if they or any of their colleagues might like some.