I've been looking for this song for awhile. I had to guess at the lyrics some because they aren't on the back of the album. The 1965 issue of It's a Small World, LP (record) Pictured here:

http://i.ebayimg.com/t/WALT-DISNEY-ITS-SMALL-WORLD-18-FAVORITE-FOLK-SONGS-ALBUM-RECORD-LP-1965-/00/s/MTIwMFgxNjAw/$(KGrHqV,!mEE8MRMnkU2BPPcQr0,3g~~60_57.JPG

This has the lyrics cited by:
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Subject: RE: Lyr Req: camp song about home in tyrol
From: GUEST,leeneia
Date: 02 Aug 08 - 11:55 AM

Great, great. I'm glad we found Stephen's song.

Now, to get back to 'Peter's fountain,' which is a rough translation of the other song we've been discussing. I believe a 'Bruenne' (sp)is a well or spring.

I sang this song as an eighth-grader in Milwaukeeland, and the words were leearned were more faithful to the original. The tune was the same as Joe's MIDI above.

Oh, I go to Peter's fountain and what do I hear?
From the misty swamp far away, cuckoo calling so clear.

'Tween Easter and Whitsuntide, all the snow melts away.
Then my girl goes and marries, leaving me in dismay.
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Except that for some un-rhyming reason, they've made the last word "Distress."

and I hear the chorus a little differently. I won't attempt to write it down. But - I have the album. So, if anyone wants here, I can try to get it into an MP3 format and put it up.

Thanks so much you all for helping me re-discover it!