You can't replace furniture because you rent?
It's built in to the bathroom, above the sink. The squeaky part is at the bottom, in a recess, which also collects any water that drips down from the mirrored door. (It does have a hole, so it won't sit there.) There is no hinge per se, just a metallic flat bottom, a metallic flange with a hole short distance above, and a thick plastic pin that goes through; the bottom flat contact between the pin (about 10mm diameter) and the painted metallic surface is what squeaks. I could add a bit of grease (something like white vaseline) every week or so, but I just hate to think of a tiny cupboard as a device that needs weekly maintenance to function without annoying noises. I'd like to try Teflon tape, the very slick surface type, if I can find some.
Replacing the cupboard is a big hassle, as the walls have a vapor barrier. So, no holes, and if any are made, they must be made to not allow water or vapor ingress into the wall. I also cannot drill any kind of holes to the outer walls, and this being a corner apartment, that's basically half of all walls here, for a roughly similar reason. This is in Finland, with a 50 degree Celsius outside temperature swing between the seasons.
[Stupid new building methods with thin films and active air pumps keeping structures dry. The same or better energy efficiency could be had by just using say 500mm of concrete and stone. Not kidding: hundred-year old apartment buildings with high ceilings and thick walls outperform new buildings in their energy efficiency here. But no, we save money, because concrete is so expensive and passé, and use all these new methods that give the house an expected twenty-five-year lifespan. Oops, wrong thread. Sorry!]
You should give a dry lubricant like graphite powder.
Good idea. For my wooden tables and surfaces, I use beeswax and mineral oil mix that I made myself. No, I'm not paranoid; I still eat canned stuff (their lining still contain BPA here). I just like the feel of wood, the ease of maintenance, and the easily repaired but tougher surface than just oiling would yield. And it is easy enough for a silly bugger like me to do.
For plastic or rubber most auto parts stores sell aerosols of a lubricant specifically for rubber and plastic and I've had good results with these.
Yup; the most annoying part of the problem is that I don't know exactly what the surfaces are. The paint could be enamel, or it could be acrylic. The plastic could be anything; it mostly feels like cheap ABS. Put the wrong stuff there that strips the paint off, or rusts the metal (whatever it is) underneath, and I need to go through the entire hassle of replacing the cupboard.
Which reminds me: You know the old-style paper-backed painters tape? It's absolutely the worst you can use for surfaces, because if you forget it, the glue will leech off from the paper backing, and somehow fuse with the surface itself, and will never ever come off. Brown packing tape does the same. I don't know if the "new-fangled" blue more plasticky type is better in that regard.