I was going to suggest American Friends Service Committee, which isn't secular. Nor is it associated with the Wim Wenders movie. They don't seem to be listed in charity navigator for some reason.

By the way, I was surprised last year to find that Habitat was "faith based". Those sneaky faithful do-gooders.

And maybe just to shake people up a bit, you could throw in a tsunami relief organization. Remind people that rebuilding and relief take a long time.