Edited to give a reason why synthetic diamonds wouldn't work instead.
In the distant future, all the diamonds are gone.
While synthetic diamonds are an excellent sollution for technology - as @ChrisJohns has noted, sometimes synthetic diamonds work best for processing, cutting etc - the jewelry industry has rejected them.
The natural mines have run dry, and laboratories will not satisfy the need for more.
Where in our Solar System can we find, and procure, more natural diamonds?
Assume the following:
- Scarcity: Earth is basically out of accessible diamonds, and we can't dig any deeper than we have been.
- Price: Natural diamonds are so expensive, due to scarcity, that interplanetary mining is a viable option at this point to acquire more.
- Necessity: A replacement material will not be accepted.
- Naturally Occuring: Synthetic diamonds have, again, been rejected by the jewelry industry: people won't feel special if their jewelry has been made in an assembly line. Even if this isn't plausible, although it should be, humor me. Answer as if I'm right, it shouldn't affect where natural diamonds can be mined.
- Abundance: The best answer will describe a location with a large amount of diamond (or maybe material to turn into diamond) that won't run out in at least twenty years of constant use
- Method: If you say "mine from Uranus because it has diamond rain" you must give a plausible explanation of how we can cut diamond at those pressures and then send it out into orbit. Yes, it's the future, but realism generally still applies.
- Specific Location: The best answer will not say "Mars has volcanoes and volcanoes have diamonds", it will say "go to this volcano and dig this deep"
- Most Economically Viable: While interplanetary mining is OK, and price of travel isn't a major concern, an answer describing mines on the moon will likely take precedence over mines on dwarf planets. Money will be spent, but less is best.