Please help identify a story about an ugly bird that would die of shame when someone looked at it

I can't figure out the title of this short story I read in the early 2000's about a bird that was so self-conscious about its ugly appearance that it would die of shame if it noticed that someone else could see it.

The bird was named after the sound it made which was a sad sound something like Yonk or Yawp or such, and I think that might have been the title of the story, but I can't find it.

The bird was also pheonix-like in that when it died by crying tears of shame, each of the tears would turn into a new bird.

I think I may have read it in one issue of Realms of Fantasy, but I'm not sure. Any information about the title and author would be appreciated.