The first thing I thought of was Oingo Boingo… I mean didn’t they and Danny Elfman kind of build an entire musical genre and career around being “Teddy Bear’s Picnic-esque”?
Here’s a completely different kind of song, but the video is populated with creepy teddy bears: “Uprising” by Muse.
A lot of the incidental music in the Banjo-Kazooie games is based on “Teddy Bears’ Picnic”. Here’s the Gruntilda’s Lair version. It does depart from the tune, but in the first two lines, it’s unmistakable.
Damn you! I knew I should have replied last night while I had the chance… (such a great tune though)