This question is not aimed for any particular period or area, just merely about the existence of the trade itself.
Were there ever any marble or stone exports?
Did a city ever find a substantial income from these exports?
How were they sold/transported? I've read of stone being on ships, but usually only as ballast.
In what form were these sold and for what purpose? (I am not asking about art per se, or the sale of statues). How economical was it to transport hulking masses of stone, especially if there was no maritime route available?
In games like Civilization, stone and marble is regarded as a valuable resource. Were there any notable nations/examples of this?
Marble from the Aegean island of Paros was quarried and widely traded as it was the highest quality marble for classical sculpting. You could start with searching for "Parian Marble" as it is known. Marble of similar quality was also quarried on Naxos.
There are literally hundreds of other quarries of various qualities and types of stone across the Ancient world, known to one or another degree of completeness.
Here is a detailed map + catalogue of many early European quarries (PDF)
I gather that social studies books no longer include maps of areas that show their valuable exports and include stone among them.
There were stone exports from at least 5000 BC. Man-carried supplies of obsidian, ochre, and such were a paleolithic trade from East Africa to the Baltic and across to the Harappan area.
"Stone" of value down the ages varied from lapis lazuli from Afghanistan shipped all over Eurasia, in beads or as boxes and other smallish items, to Carrara marble shipped out of Italy to sculptors all over Europe (Carrara is a town that lives off its quarries, like some towns in Vermont). Stone can be your local sandstone for massive structures, or slate for roofs (it splits into shingles nicely), or colored granite to face a building of concrete, brick, or lesser stone.
It's hard to find some place wealthy enough to build in imported stone that isn't within sight of a seaport or navigable river. Water transport is always the best for heavy cargoes. That's why canals were built in the 1700s and 1800s, because animal-powered land travel limited haulage.
Where special stones had to be brought overland, economy was usually not as important as someone's ego, like a king or millionaire. Stones would be cut down to the size of facing slabs or the like, and no larger than, say, what a camel could carry a pair of. Oxen hauling stoneboats are what we see the Egyptians using to pull obelisks, blocks, and statues into place. Oxen are remarkably strong for hauling. Much more efficient than slaves. Note that obelisks were single blocks: big items.
As well, if someone will pay the price, it is always "economical" to haul anything to where the buyer wants it. Having to take two months to drag it overland just ups the price: it doesn't make it impossible.
Again, the Egyptians left us pix of taking stone off river ships, with counter-weighted derricks of necessity. Carving the stone in advance made it lighter: you weren't transporting the waste stone to the final locale.
"The bluestones at Stonehenge were placed there during the third phase of construction at Stonehenge around 2300 BC. ... The stones are estimated to weigh between 2 and 4 tons each. The majority of them are believed to have been brought from the Preseli Hills, about 250 miles away in Wales." (Wikipedia)
Ancient people weren't shy about hauling big things. I think we can call that an export, and an overland transit.