Perhaps a slight turn of thought (and just a touch of fun) is required. We could drop the Latin for some of the planets and look at Greece for the original names of the Roman gods chosen to represent them. On the other hand, just one of them uses a Latin derivative, as with "Jovan moons," "Jovan asteroids," and "Jovan LaGrange points" (by Zeus ... I mean, Jove). From the late 14th century, Jove had become a poetic term for the planet Jupiter, stemming from the Latin Iovis.
From the inner orbit outward:
Mercury might take sub-mercurian/sub-mercurial or sub-hermitian (very doubtful on the last one – a bit rough on the artistic flow).
Venus might prove difficult using the Greek Aphrodite, and sci-fi writers have already leaped upon the term Venusian (capitalized). It sounds pretty solid.
I'm sure a truly 'solar' language will have to glimpse some of the original Greek. I found that NASA did just that when I visited some of their many informative pages regarding the planet Mars. There, they used the term areocentric to describe a Mars orbit. Roman Mars equals Greek Ares, ergo areocentric. The word seemed to flow for me with a pleasant grace. In this venue, could underground on Mars become sub-arean? The term terrain might even reach as far as, dare I say it ... areain...?
For Jupiter, it seems to be stuck with Jove, a Latin derivative, so below the surface clouds of Jupiter might be found sub-Jovan (capitalized again).
Saturn will likely stick with Saturnine (so many capitalizations) cloud cover and, therefore, sub-saturnine (NOT capitalized - yay!).
The sniggering joke of the planets, Uranus, is already linked to Uranian.
Apparently, Neptune may go either way, with the accepted adjectives Neptunian and Poseidean.
Pluto, our newest non-planet (aka dwarf-planet) already uses the adjective Plutonian. Considering the Grecian Underworld to be the home for both Heaven and Hell in Greek mythology, might sub-Seventh Heaven also apply? Sub-Cloud 9? Naw. Just sub-Plutonian (capitalization required).