Organic gemstone-like compound

Organic gemstones shall include all gemstones that ...

• ... do not contain metals but only light non-metallic elements
• ... do contain carbon

Typically These ...

• ... contain volatile elements (carbon, nitrogen)
• ... are combustible.
• ... become unstable if too much oxygen (or sulfur) is mechanosynthetically added

List of organic gemstone compounds (attempting exhaustiveness)

The options are rather limited so it seems here (for once) one quickly can arrive at a quite exhaustive list of the most basic possible structures.
As always on this wiki: The heavier more scarce elements (Arsenic, Selenium, ...) are excluded for materials for eventual large scale structural use.

• Diamond
• Lonsdaleite
• Beta Carbon Nitride – (possibly a fire hazard)
• Stretching it a bit Boron carbides like Terraboron monocarbide
• Likely some carbon phosphides (at least sheets) – eventual health hazard due to direct carbon phosphorus bonds (common in toxins)

Why adding oxygen or sulfur only works for trace amounts

• Adding oxygen in high quanity leads to carbon dioxide CO₂ which is (as one should now) not stable as a covalently cross-linked solid
• Adding sulfur in huge quantity leads to carbon disulfide CS₂ wich is an (interesting) liquid in its thermodynamic stable form
• Nitrogen just wants to mind it's own business and wants to get back to its molecular di-nitrogen from with its strong tripple bond (usually a quite exoergic reaction)

Metastable solid state forms (not referring to being frozen) may be possible (especially at low temperatures) but activation energies are low making these compounds into dangerous high energy explosives.

Dropping the condition on containing carbon

Including compounds without carbon one gets the
slightly bigger class of metal free gemstone-like compounds.
These include:

• BN Boron nitride – likely incombustible
• BP Boron phosphide – incombustible

Adding sulfur – This time it works – somewhat

Adding a sulfur into the mix in high ratio does not make the metal and carbon free gemstones unstable (decomposing to gasses) immediately
but does instead lead some quite exotic stuff crossing over to polymeric nature:

• B₂S₃ Boron sulfide (wikipedia)

Phosphorus sulfides from many stable stiff highly cross-linked molecules. E.g.:

• P₄S₁₀ Phosphorus pentasulfide – interrestingly this has diamondoid structure but it's limited to one molecule
• P₄S₃ Phosphorus sesquisulfide

Sulfur nitrides from many (somewhat) stable structures. E.g.:

• S₄N₄ Tetrasulfur_tetranitride (shock sensitive)
• (SN)_x Polythiazyl
• (S)_x Elemantal sulfur in form of long chains polysulfanes