How big is a diamond molecule?
I put this question in IMHO and not FQ because I believe any response will be more like an opinion than a fact.
I beleive that your premise is inaccurate as a diamond is not a singular molecule, but a molecular structure of carbon molecules. Perhaps more accurate to discuss crystal size.
If the diamond is a single crystal, then the whole thing is one molecule. All of the carbon atoms are connected together via covalent bonds. That might seem weird, but there are lots of arbitrarily large macromolecules. Rubber, for example, can be one extensively cross-linked molecule.
I think it a debatable issue whether it’s more sensible to call it one huge molecule or just to say it’s not molecular.
Can you have a mole of white dwarfs?
https://www.nationalgeographic.com/science/article/diamond-the-size-of-earth
Diamond, of course, has a crystalline structure, but it makes perfect sense to look at a single cubic cell of this structure and measure the length of a side: 3.57 Å, which seems pretty small considering it is not a close-packed structure, compared to silicon (5.43), germanium (5.66), tin (6.49) in the carbon group.
Crystalline solids are not what I’d call molecular.
Carbon can form monoatomic molecules - buckminsterfullerene is molecular, for instance. But diamond and graphite are not.
Simple test - can you tell me the mass of a mole of diamond? Not a mole of carbon, mind you. A mole of diamond.
Assuming it’s life-sized, about 3.5x the mass of a regular mole. 
As big as the Ritz.
Allow me to attempt to restate the OPs question then.
How large is the smallest collection of carbon atoms that would be identifiable as a diamond?
My quick search indicates it would be this structure (not to scale).
That was already answered:
That’s the lattice constant for diamond.
Natural diamonds have impurities in them, so the molecular definition of “diamond” is imprecise. (Most artificially-made diamonds, being much more pure, react differently to UV light.)