I've had some luck with the search engines Google and AllTheWeb.com... when I add the qualifier ".wav" or ".mp3" to the animal's name.
Findsounds.com used to work better than it does lately. Doesn't search for .mp3s. Maybe hasn't been updated in awhile???
Still have yet to find a decent downloadable rabbit-in-distress sound anywhere on the web, myself. This is without question the basic meat-n-taters noise, the go-to call, the one absolutely essential sound, for predator calling. If you don't have a good tape or a CD of a cottontail distress, do yourself a big favor and plunk down $10 or $20 to buy one. If only to have an idea of what you--or the old-boy-blowing-on-a-tube track you just cadged off the web--should be imitating!
LionHo