I don't know how serious it is, but apparently one of the proposals is to grow trees (capturing the carbon) and then cut them down and bury the lumber. Which sounds laughably expensive to me.
(Then there's the carbon put out by whatever you use to industrialise this process (unless it's a Mr Fusion!?!) which needs offsetting, that hopefully is no more problematic than the Rocket Equation mathematics.)
...There's a lot of old wooden pit-props in old mines, I suppose you could just cram in even more, floor-to-ceiling, and (sort of) 'refill' what's left of any (uncollapsed) mines. Coal for the next Millenium! (Or one a number of millenia hence.)
Of course, even the intact levels will be squashed somewhat, already, and those seams that were taken out were pre-squeezed by the oroginal coal-forming processes, so (without a lot of 'anti-subsidence'-causing jacking up/geoengineering) you're never going to completely undo the extraction humanity once did. And if someone far enough in the future (amnesiac humanity, or its post-anthropocene successor) ever tries to exploit the neo-coal reserves, for reasons we may perhaps assume to be naive shortsightedness, they'll get a few puzzles that their geologists may have to work out, or eventually call in their version of paleoanthropologists to properly explain/argue over.
But also you have to make sure they don't rot! Which led to the podcasters joking about using the same hole as a nuclear waste dump. Wild stuff.
Rotting isn't all bad, if it just seeps[1], although it is true we don't know what problems we're storing up for the future. But it could be better (FCVO 'better') than pumping CCed gas straight back into fuel-gas (methane/etc, not gasoline, for AmeriPol disambiguation!) pockets that we tapped into.
The advantages of gas-pockets is that we now know many of them that obviously
were gas-impermeable for a very long time, deep down well below most freak-but-natural erosion events[2], which is why they were there to be tapped.
If we can ensure our own extractive puncture isn't going to be a problem to the future se, or the microsubsidence that might have been caused by releasing the intersticial gasses (then 'reinflating' the pores) then it's probably easier to pump gas of our own back in through the pipe incrastructure already set up. But if it fails to hold (during or after refilling) it'll be a comparative
rush of gas, exactly of the kind(s) we didn't want in the atmosphere, undoing all the hard work for that particular basket of eggs quite rapidly! Though (even 'deep') coalmines (or saltmines[3], etc, to confuse the future-geologists even further!) aren't perhaps provably gas-sealed as gas-pockets, there's nothing (if you can prevent or quash ignition, perhaps by raising CO
2 levels down there
as well) that can create such a potentially catastrophic outgassing of all you put in.
Buildings, is one big suggestion. More wooden-framed buildings. They have their own hazards (
Grenfell, but not just cladding; or as highrises are unlikely with much wooden structure,
Tokyo/
London/etc low-rise widespread fires in general) but with modern methods and rules
should (again, c.f. Grenfell), and without deliberate intent (c.f. Tokyo, but also far-less-totally woody Dresden) be mitigatable.
Concrete is far less flammable, but it and its fellow materials are huge carbon-sources in manufacture (there's work towards carbon-sink, or at least partly-resequestering, versions). There was a recent call by architects, perhaps in the UK, to do more refurbishment of old concrete structures
rather than making the old one ('expensively' produced, carbon-wise if not in any other way) into rubble and then building new ones (a new splurge of industrial-strength effort) that might be intrinsically green (more passive 'climate' control, rather than add-on AC running constantly) but be less so if you amortise with the demolition that came beforehand.
These are all ongoing questions. As is how the balance of building new wooden structures on brownfield sites (or even greenfield sites, at best 'only' surrendered from the stranglehold of agricultural monoculturism) going to help in both satisfying much needed housing issues
and net-zero aims (adding additional transportation to that mix, probably, unless we encourage greater home-office working - for suitable professions - in the useful shadow of Covid).
Sorry, I originally had just two points (shoving wood in mines, and more (sustainable!) wooden-buildings, as a couple of sequestering methods to compare), but it ran away with me.
[1] Methane is one of the gases that degrades under sunlight, given enough time, making it a good marker for "something going on" that
might be life in exoplanetary research - but not as good as copious oxygen, like ours, assuming the similar trick to photosynthesis gets invented and sustained in that world's tree-of-life, too.
[2] It is said the biblical 'burning bush' was inspired by a natural seep of near-surface hydrocarbons find itself venting and naturally ignited, possibly
in front of an actual bush so that it was visually indistinguishable to someone sucficiently credulous - at least for long enough to create the story. And, hydrocarbon seeps being important hallucinogens in classic oracular temples, the unburnt stuff coming up under the observer's feet might have added to the prophetic mix, who just happened to be there in the middle of nowhere for the relatively short-lived escape (and partial ignition) of gasses.
[3] Proven at least to be waterproof, or else they'd be brinepits! (As some have indeed become, after unwise human interference with other local bitz of geography/geology.)