buy a cheap tlr like a yashica A or some other steel bodied tlr and stretch some saran wrap over the lens (you can fasten it around the lens with rubber bands). apply petroleum jelly until the image degrades to that of a holga.
You could apply the jelly to a filter too, just don't put it on the lens proper.
How about an old zeiss Ikon 515? Soft lens, bellows will likely be rotted out, you can patch it with gafers tape and "choose" where and how much light to leak.
Take a look over Gene's site for starters. Check in the found film section as well.
You could try a box camera, if you can find one that does 6x6 - many are 6x9 or 6x4.5. There are a number of bakelite and folder cameras with very basic shutters and lenses that would suit.
For simplicity, I like my Box Tengor, but that may be too good a quality...
Sorry for the delay in replying to these suggestions, I've been busy researching all these models. Some of these cameras I hadn't heard of. And I'm looking at a few more like the Ilford Sporti and Super Sporti.
Not that common I guess, but my Ferrania Eura fits the bill as a Lo-Fi camera with one shutter speed, two f/stops (f8 and f12), a tripod mount, flash sync post and a good film transport. Actually takes quite decent photos as it is, but removing the film mask will get you closer to the vignetting Holga-land bliss. And a bit of black tape covers the red window in the back.