I have some too and recently showed them in a video... In it I suggested I might make them into kitchen magnets to giveaway Doh! Never mind...mine are zinc plated!
Well, you could bake out the mercury (OUTDOORS) -- yeah, it would go into the atmosphere, but that's not much mercury, and it would dissipate really quickly. Or, if you want to be more responsible, go get a bag of sulfur at the hardware store, melt some in an old tin can, and roll it around to coat the sides. Then dump in the cents, and fill the can with more melted sulfur. It ought to react with the surfaces of the cents, both the copper and the mercury, and turn it into non-volatile sulfides. At that point, it ought to be pretty stable, unless it gets incinerated.
Put them in a bag labeled "contains mercury" in a box with fluorescent light bulbs, take them to where you dispose of fluorescent light bulbs.
I'll be honest.... I've never bought or disposed of a fluorescent bulb (well, we use them at work... but there's a "disposal box" and I don't think about it). The puppy-dog's recommendation is actually easiest - the nearest disposal for mercury-containing items is only a couple miles from my house, so I'll just take them there.
I can remember kids covering quarters with mercury from the science lab in junior-high. It’s a miracle any of us are alive today. https://www.epa.gov/mercury/storing-transporting-and-disposing-mercury
They look like normal cents to me, maybe polished. Where is the indication they were plated? Serious question.
Find a local waste incinerator. They have the pollution control equipment to contain the mercury fumes.
Pretty sure that's exactly backwards. The most effective way to control mercury emissions from waste incinerators is keeping it out of the waste stream. I like the suggestions to put it in with fluorescent bulb waste or mercury thermometers. In both those cases, the disposal chain is set up to capture and sequester mercury. We're probably only talking about a few tens of milligrams of mercury here, the equivalent of a box of CF bulbs. But if there's a cheap and easy way to keep it from getting into the environment, it's good to take advantage of it.
I had a comment, but decided it would be taken totally the wrong way, so I'll keep my pie hole shut, well at least until I'm done chewing my pie.