The lifeforms don't have to use hydrogen sulfide as a solvent. Maybe they've got an internal water-ammonia eutectic mixture or something; anyway, it doesn't matter. The point is, I want an ocean of cryogenic hydrogen sulfide, and I want some kind of creatures living in/by it.
Thought one: maybe it could be a carbon planet, because water is unstable on carbon planets, and there wouldn't be oxygen to burn the hydrogen sulfide, so that would let a small amount of hydrogen sulfide collect in seas without being totally overwhelmed by water.
Except... carbon has a higher affinity for hydrogen than sulfur does, so hydrogen sulfide isn't actually geologically stable on carbon worlds, either.
Thought two: maybe its a really small world, like Io, such that the lightest volatile chemical it could hold on to during formation was hydrogen sulfide.
Except, if there are lifeforms there (and no oxygen, because hydrogen sulfide, and no atmospheric hydrogen, because small world that can't hold onto it), then it will be energetically favorable for heterotrophs to strip the hydrogen off of sulfur to produce methane--and both methane and H2S are easily photolyzed (because no ozone layer, because no oxygen), so hydrogen will be lost, carbonaceous biomatter and H2S will be converted into methane and solid sulfur, more hydrogen will be lost, and the sea will dry up.
Thought three: maybe it's just a really cold, otherwise Earthlike world, where water is frozen out.
Except, water and H2S form a relatively high-temperature gas clathrate, so water ice would just trap all of the H2S, unless there's a truly enormous quantity of it.
So: is there a plausible way to get a sea (it doesn't have to be a huge ocean, just definitely "sea" sized) of hydrogen sulfide, which is geologically stable, on a world with lifeforms of some sort?