It's indeed the case that the comparative lack of rotting during carboniferous contributed to the available biomass to turn into coal, but that sort of coal doesn't form without heat and compression. It's got as much to do with the earth being more geologically active at the time, and more low-lying wetlands.
But coal is forming today from peat -> lignite -> bituminous coal -> anthracite (then eventually graphite). E.g. Germany's electricity generation was ~30% lignite burning in 2015[1], and those deposits formed mostly during the tertiary period.
So you're five to six orders of magnitude off if you think coal hasn't been forming since the carboniferous.
None of which is to say that these deposits are renewable in any practical sense. We can imagine digging them all up and burning them in the next 500 years, and then having to wait around the time since the T-Rex walked the earth for meaningful regeneration.
This is simply untrue.
Grow woody biomass, and combust it in a reducing environment, and you get carbon. It's biologically inert. Bury it.
It's not difficult, or impractical, and even if you mix it into soil, it will remain sequestered for centuries or millennia.
It's just... charcoal. Why would we have to make coal in the way it was made in the carboniferous? Your doom posting doesn't make any sense.
If such a carbon reduction is desirable, then taxes on air travel need to be raised.
It is very easy if you travel by plane several times per year, even on short distances, and you just stop to do that. In fact, it is probably the most effective thing you can do to reduce your own lifetime carbon footprint. A single two-hour flight produces around 400 kilograms of CO2 per person. This is equivalent to several months of heating in a cold country.
And don't start me harping about "offsetting" carbon emissions. Carbon has been captured in the course of hundreds of millions of years. There is nothing humans can do which can store it again for the same time. Almost all carbon from a tree is released when the tree dies.
In fact, it is even worse for coal. The coal deposits which we still exploit today, against all better knowledge, have mostly been formed during the carboniferous geological period. In this period, there were NO bacteria and fungi which could decompose lignin, the main structural component of wood. In other words, the wood from trees could not decay, which was the base for the coal deposits from the carboniferous period, which still form most of the coal today. The consequence of this is that burning coal is irreversible even in the course of tens of thousands of years, because the conditions under which this coal has been formed - an absence of fungi that can decompose lignin - simply do not exist any more. We are not only doing massive damage to the next generations of human children, but we are profoundly and irreversibly changing the conditions for life on Earth.